The copper rods swing freely, and will be attracted or repelled from each other depending on the currents passing through them. What is the magnetic force between wires formula? A third current-carrying wire parallel to both of them is placed in the same plane such that it feels no net magnetic force. For part a, since the current and magnetic field are perpendicular in this problem, we can simplify the formula to give us the magnitude and find the direction through the RHR-1. [/latex], [latex]\frac{F}{l}=\frac{\left(4\pi \phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{7}}\text{T}\cdot \text{m/A}\right){\left(1\phantom{\rule{0.2em}{0ex}}\text{A}\right)}^{2}}{\left(2\pi \right)\left(\text{1 m}\right)}=2\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{7}}\phantom{\rule{0.2em}{0ex}}\text{N/m}. Some of our partners may process your data as a part of their legitimate business interest without asking for consent. This tool provides accurate and instant The space or region around the current carrying wire/moving electric charge or around the magnetic material in which force of magnetism can be experienced by other magnetic material is called magnetic field or magnetic induction by that material or by that current. Generally, magnetism is a property shown by magnets and produced by moving charges, which results in objects being attracted or pushed away. This formula for the magnetic force on a current carrying wire is the basis for the experiment that was used to define the ampre from 1948 to 2019. . Only the sides of the square parallel to the inifinite wire contribute to the force. Problem 4: The length of two wires is 0.5 m and the distance between the wires is 1m. In this section, we will learn about this case which is in further detail. Thus we can pen it down as follows: Q1. calculations simply at a faster pace in just a fraction of seconds. Follow the where r is the distance between segment of loop 1 and segment of loop 2; and is a unit vector that points along the line connecting the two segments, from loop 1 to loop 2. o = 4 x 10 -7 Tm/A Problem 5: Wire P carrying current 6 A upward and wire Q is 1m apart from it. As mentioned in the previous chapter, any physical quantity, such as the direction of the force exerted on a wire, will always depend on two successive uses of the right hand. The force is attractive if the currents are in the same direction, repulsive if they are in opposite directions. If current I 2 = Amperes Also, What force do they exert on each other? The force on current carrying wire in a magnetic field is F = (length of wire)*IxB = (lenght of wire)*I*B*sin (theta). Ans: So if we have two current-carrying which are said to be parallel wires with magnetic fields circling that are around them in the direction which is same, they will attract each other which is at the point at which their respective magnetic fields intersect. At least Flash Player 8 required to run this simulation. A charge is a basic property associated with the matter due to which it produces and experiences electrical and magnetic effects. say we have two long infinitely long imagined current carrying wires separated by some distance d then we know that these wires are going to generate their own magnetic fields the magnetic fields will of course be everywhere but here's the thing current carrying wires inside a magnetic field experience a force so this wire second wire will experience the force due to the magnetic field . Problem 3: Two very long wires are placed parallel to each other and separated by a distance of 1m apart. guidelines and rules to get the output easily. If 1 A current is passed in the wires in the same direction, the force per unit length between the wires is: Current flowing in each wire (I1 and I2) = 1A. It is only apparent if the overall charge density is zero; otherwise, the Coulomb repulsion overwhelms the magnetic attraction. rectangular loop carrying current Iz in the What; is the net force (magnitude and direction) of the: force exerted on Squarc: loop by the line current. with our handy calculator. Click on "Show Forces" to see the resulting . Ans: As we have already seen that it is carrying current which is known as the DC, that is some flux lines which will be generated that too around the conductor and they are concentric which is with the central axis of the conductor. [/latex] For both the ampere and the coulomb, the method of measuring force between conductors is the most accurate in practice. The force thus created between two wires defines the fundamental concept of ampere. 2 Magnetic field problems Consider infinite wire carrying current H- Beside the wire direction shown. When currents flow in the same direction, the magnetic field is polarised and the wires attract. If so, then we can ask what is its direction? There are two long wires aand bcarrying currents Ia and Ib respectively, separated by a distance d, then the force on a segment of length Lof bdue to ais Fba =Ib LBa =2d0 Ia Ib L LEARN WITH VIDEOS Force between Parallel Current carrying Wires 6 mins Quick Summary With Stories In large circuit breakers, such as those used in neighborhood power distribution systems, the pinch effect can concentrate an arc between plates of a switch trying to break a large current, burn holes, and even ignite the equipment. Forces Between Two Current-Carrying Wires. For both the ampere and the coulomb, the method of measuring force between conductors is the most accurate in practice. Then suppose the two long straight wires run perpendicular to each other without touching. The gauge pressure inside the pipe is about 16 MPa at the temperature of 290C. Magnetic Force: . = 360 x 10-7/11if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[250,250],'physicscalc_com-leader-1','ezslot_8',110,'0','0'])};__ez_fad_position('div-gpt-ad-physicscalc_com-leader-1-0'); Therefore, the magnetic force between two wires is 32.7272 10-7 Moving charges generate an electric field and the rate of flow of charge is known as current. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Contents of this article: Expression for magnetic force; . We need to Justify our responses by using the right-hand rule. A circuit with current I has two long parallel wire sections that carry current in opposite directions. This also provides us with a method for measuring the coulomb. access violation at address A volt, according to BIPM, represents the "potential difference between two points of a conducting wire carrying a constant current of 1 ampere when the power dissipated between these points is equal to 1 watt." The symbol for volt is "V." Simplified, this means that voltage, compared to water pressure through pipes . The direction of the magnetic field which downwards due to the first conductor. The magnetic field at a certain point due to an element l of a current-carrying conductor is. Angles can be measured in degrees or . Apr 1, 2006. Identify the Problem Any time you are asked about EMF or current in a loop (real or imagined), you have electromagnetic induction during any period of time in which the amount of magnetic flux through the loop changes. The force on an electric charge q due to both of them can be written as, F = q [E(r) + v B(r)] EElectric + Fmagnetic. Fig. The ratio F/l is the force per unit length between two parallel currents [latex]{I}_{1}[/latex] and [latex]{I}_{2}[/latex] separated by a distance r. The force is attractive if the currents are in the same direction and repulsive if they are in opposite directions. flows in the second wire. acknowledge that you have read and understood our, Data Structure & Algorithm Classes (Live), Full Stack Development with React & Node JS (Live), Fundamentals of Java Collection Framework, Full Stack Development with React & Node JS(Live), GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Difference between Center of Mass and Center of Gravity, Difference between Wavelength and Frequency, Differences between heat capacity and specific heat capacity', Difference between Static Friction and Dynamic Friction, Relation Between Frequency And Wavelength, Difference between Voltage Drop and Potential Difference. when the current in both wires is doubled. (c) What happens if the currents flow in opposite directions? Question 2: Calculate the force on the wire, given B = 1.50 T, l = 5.00 cm, and I = 20.0 A. Divide the product from above step by the product in step 2 to get the sun ray. So we can say that an electromagnetic field is established that too due to this current through this conductor. Viewgraph 3 . Magnetic Force Between Two Parallel Current Carrying Wires, Physics & Electromagnetism 123,407 views Dec 19, 2017 This physics video tutorial explains how to calculate the magnetic force between. We might not generally expect that the force which is between wires is used to define the ampere. It is placed at a distance of. force between parallel wires calculator uses magnetic force per unit length = ([permeability-vacuum]*electric current in conductor 1*electric current in conductor 2)/ (2*pi*perpendicular distance) to calculate the magnetic force per unit length, the force between parallel wires formula is defined as the force of attraction or repulsion between 0. So options 3 and 4 are wrong. = 0 4 i r r 3. B is in a direction normal to the plane of . Force between two parallel Current carrying conductor We have learned about the existence of a magnetic field due to a current-carrying conductor and the Biot - Savart's law. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. In each of these examples, a mass unit is multiplied by a velocity unit to provide a momentum unit. As specified by the Lorentz force formula, an external magnetic field exerts a force on a current-carrying conductor. It is also called the Lorentz force. Problem 6: Wire A and B are 1m apart. Located at: https://openstax.org/books/university-physics-volume-2/pages/12-3-magnetic-force-between-two-parallel-currents. The force which is between two long straight conductors and the conductors which are parallel as well and separated by a distance r can be found by applying what we have developed in preceding sections. From previous studies, we can say that conductor 2 experiences the same magnetic field at every point along its length due to conductor 1. By the end of this section, you will be able to: You might expect that two current-carrying wires generate significant forces between them, since ordinary currents produce magnetic fields and these fields exert significant forces on ordinary currents. The first wire will create a magnetic field, \(\vec B_{1}\), in the shape of circles concentric with the wire. Consider two infinite parallel straight wires, a distance \(h\) apart, carrying upwards currents, \(I_{1}\) and \(I_{2}\), respectively, as illustrated in Figure \(\PageIndex{1}\). This also provides us with a method for measuring the coulomb. distance between the wires in the input fields of the calculator. Compare and contrast the electric field of an infinite line of charge and the magnetic field of an infinite line of current. Here F/L physics concepts calculators to solve the lenthy & difficult Two parallel wires carry current in opposite directions, as shown in Figure \(\PageIndex{2}\). The first wire is located at (0.0 cm, 3.0 cm) while the other wire is located at (4.0 cm, 0.0 cm) as shown in Figure 12.10. N. Physicscalc.Com offers various When two current-carrying conductors carry current in opposite directions, they will repel each other. Since [latex]{\mu }_{0}[/latex] is exactly [latex]4\pi \phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{7}}\phantom{\rule{0.2em}{0ex}}\text{T}\cdot \text{m/A}[/latex] by definition, and because [latex]\text{1 T}=1\phantom{\rule{0.2em}{0ex}}\text{N/}\left(\text{A}\cdot \text{m}\right),[/latex] the force per meter is exactly [latex]2\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{7}}\phantom{\rule{0.2em}{0ex}}\text{N/m}. We are migrating to a new website ExamFear.com is now Learnohub.com with improved features such as Ask questions by Voice or Image Previous Years QuestionsNCERT solutions Sample Papers Better Navigation A . Due to relative length contraction, if the currents flow in opposite directions, the electrons have an increased density of electrons in the other wire. Recently, the definition was updated to be based on defining the Coulomb in such a way that the elementary charge has a numerical value of \(e = 1.602 176 634 10^{19}\text{C}\), and the Ampere corresponds to one Coulomb per second. You can verify that you get the same answer if you, instead, use your left-hand to define the direction of the magnetic field (which will be in the opposite direction), and then again for the cross-product. Answer (1 of 3): Looking at the comment and the picture this is a very common and tough homework or exam type problem. . This force is responsible for the pinch effect in electric arcs and plasmas. What Do You Mean By Current Carrying Conductor? The force per unit length from wire 2 on wire 1 is the negative of the previous answer: These wires produced magnetic fields of equal magnitude but opposite directions at each others locations. The infinite, straight wire shown in the accompanying figure carries a current [latex]{I}_{1}. So we can see that conductor which is in the 1 experiences the same force that is generally due to conductor 2 but the direction which is in the opposite. In contrast, when these two current-carrying conductors carry current in the same direction, then they attract each other. In the figure, we can see the wires and their currents fields which they generally create and the subsequent forces they exert on one another. Figure 3. Similarly, we can calculate the force exerted by conductor 2 on conductor 1. magnetic force. Question: If 12 A of current flows in the first wire, 15 A of current F/L is the force per unit length acting on each wireif(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[250,250],'physicscalc_com-banner-1','ezslot_9',108,'0','0'])};__ez_fad_position('div-gpt-ad-physicscalc_com-banner-1-0'); o is the permeability of free space that has a constant value. The movement of charges generates magnetism around a conductor. 6 mins. Therefore, the force per unit length between two parallel conductors is given by the expression: f = F L = 0 4 2 I A I B d The direction of the force can be calculated by using the Fleming's Left Hand rule where: i) Index finger represents the direction of the magnetic field, B ii) Middle finger represents the direction of the current, I F / l is the force per unit length between two parallel currents I 1 and I 2 separated by a distance r. The force is attractive if the currents are in the same direction and repulsive if they are in opposite directions. Before 2019, the Ampere was defined to be that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one meter apart in vacuum, would produce between these conductors a force equal to \(2 10^{17}\text{N}\) per meter of length. On a section of length, \(l\), of the first wire, the magnetic force from the magnetic field, \(\vec B_{2}\), has magnitude: \[\begin{aligned} F_{1}=I_{1}||\vec l\times\vec B_{2}||=I_{1}lB_{2}\frac{\mu_{0}I_{1}I_{2}}{2\pi h} \end{aligned}\]. This is the basic concept in Electrostatics. The consent submitted will only be used for data processing originating from this website. Wire P carrying current 1A. Then, the ratio B1 /B2 is Medium View solution What is the nature of force between two parallel conductors carrying currents in the direction? Ans: When the flow of the currents is in the same direction, the magnetic field will be opposite and the wires will attract. As mentioned in the previous chapter, any physical quantity, such as the direction of the force exerted on a wire, will always depend on two successive uses of the right hand. The field due to [latex]{I}_{1}[/latex] at a distance r is, This field is uniform from the wire 1 and perpendicular to it, so the force [latex]{F}_{2}[/latex] it exerts on a length l of wire 2 is given by [latex]F=IlB\mathrm{sin}\phantom{\rule{0.1em}{0ex}}\theta[/latex] with [latex]\mathrm{sin}\phantom{\rule{0.1em}{0ex}}\theta =1\text{:}[/latex], The forces on the wires are equal in magnitude, so we just write F for the magnitude of [latex]{F}_{2}. There seems to be a pretty standard formula, that if a wire of length carrying current I is immersed in a magnetic field B, then the magnitude of the magnetic force is F B = I B s i n , where the direction of F B is the direction of B (determined using right-hand rule). When two wires carrying a d.c current are placed parallel to each other then there always will be a magnetic force acting between two wires. 1.4 Heat Transfer, Specific Heat, and Calorimetry, 2.3 Heat Capacity and Equipartition of Energy, 4.1 Reversible and Irreversible Processes, 4.4 Statements of the Second Law of Thermodynamics, 5.2 Conductors, Insulators, and Charging by Induction, 5.5 Calculating Electric Fields of Charge Distributions, 6.4 Conductors in Electrostatic Equilibrium, 7.2 Electric Potential and Potential Difference, 7.5 Equipotential Surfaces and Conductors, 10.6 Household Wiring and Electrical Safety, 11.1 Magnetism and Its Historical Discoveries, 11.3 Motion of a Charged Particle in a Magnetic Field, 11.4 Magnetic Force on a Current-Carrying Conductor, 11.7 Applications of Magnetic Forces and Fields, 12.2 Magnetic Field Due to a Thin Straight Wire, 12.3 Magnetic Force between Two Parallel Currents, 13.7 Applications of Electromagnetic Induction, 16.1 Maxwells Equations and Electromagnetic Waves, 16.3 Energy Carried by Electromagnetic Waves. Two parallel wires carrying equal currents in opposite directions are placed at x=aparallel to y-axis with z=0. [/latex] This is the basis of the definition of the ampere. Medium View solution > Thus, we can say that any two current-carrying conductors when placed near each other, will exert a magnetic force on each other. where,d is the distance between two conducor,Ia is the current in a conductor,Ib is the current in b conductor, Problem 1: Two long parallel wires separated by 0.1 m carry currents of 1A and 2A respectively in opposite directions. So if we have two current-carrying which are said to be parallel wires with magnetic fields circling that are around them in the direction which is same, they will attract each other which is at the point at which their respective magnetic fields intersect. Answer: The force on the current carrying conductor is given by, F = ilBsin ( ) Where, i = 20A, B = 1.5T and l = 5 cm and = 90. We can notice that the two loops of wire carrying currents can exert forces and torques on one another. Thus, from the two studies that we can say that any two current carrying conductors that when placed near each other will exert a magnetic force that is on each other. The magnitude of the force acting between two parallel current carrying conductors is calculated using: Where: is the force per unit length between the conductors (in Nm 1) is the magnetic permeability of free space (4 10 7 NA 2)* is the current in wire 1 (in A) is the current in wire 2 (in A) is the distance separating the . Multiply the values of current flowing through two wires with the So we can say that if electrons are there in both wires which are said to be moving in the same direction they see the same number of electrons in the other wire that is because they are moving at the same speed. Magnetic field produced on wire 1 by wire 2 is, B21 = 0I1 / 2r = 410-71 / 21 = 2 10-7 T. Magnetic field produced by wire 2 on wire 1 is, B12 = 0I2 / 2r = 410-71 / 21 = 2 10-7 T. Force (F1) and (F2) is acting on wire 1 and 2 respectively, B12 is directed to the right side and B21 is directed to the left side. Eddy currents (also called Foucault's currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction or by the relative motion of a conductor in a magnetic field. Both have a force per unit length of [latex]9.23\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{12}}\phantom{\rule{0.2em}{0ex}}\text{N/m}[/latex]. The angle between the current and the magnetic field is 90. a. But, these properties can all be summarized into the equation is the force per unit length, d is the distance between wires, Ia and Ib #2. barob1n. (Since the two wires are parallel the field of one strikes the other at a right angle and the cross product reduces to straight . the magnetic force quickly and easily. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. There will be no force, since the currents cancel. Magnetic fields exert force on the moving charges and at the same time on other magnets, all of which have moving charges. The top wire carries a current I2 through the magnetic field B1, so (by the Lorentz force) the wire experiences a force F12. The force between two wires is a good system to understand how any physical quantity cannot depend on our choice of the right-hand to define cross-products. For example, the force between two parallel wires carrying currents in the same direction is attractive. Which we can see is the three parallel coplanar wires with currents in the outer two in opposite directions. Explain Why Two Current Carrying Parallel Conductors Attract. Example Definitions Formulaes. As we have already seen that it is carrying current which is known as the DC, that is some flux lines which will be generated that too around the conductor and they are concentric which is with the central axis of the conductor. Two long, straight wires are parallel and 25 cm apart. Manage SettingsContinue with Recommended Cookies, Magnetic Force Between Current-Carrying Wires Calculator gives output as Previously we have learned about the existence of a magnetic field that is due to a current-carrying conductor and the Biot Savarts law. We see that conductor 1 experiences the same force due to conductor 2 but the direction is opposite. Section Summary Thus. Then in the figure that is (b) a view which is from above of the two wires that are shown in (a) with one magnetic field line which is shown for each wire. [/latex], [latex]r=\sqrt{{\left(\text{3.0 cm}\right)}^{2}+{\left(\text{4.0 cm}\right)}^{2}}=\text{5.0 cm}. The distance between two wires is 11 m and Current-Carrying Wires Calculator? Here the term that is RHR-1 shows that the force which is between the parallel conductors is attractive when the currents are in the same direction. The density of magnetic field lines indicates the strength of the magnetic field. From the free-body diagram in the figure, the tensions in the supporting leads go to zero when the gravitational and magnetic forces balance each other. Calculating Forces on Wires Two wires, both carrying current out of the page, have a current of magnitude 5.0 mA. In this system, we first used the right-hand rule for axial vectors to determine the direction of the magnetic field from one of the wires. [latex]F\phantom{\rule{0.1em}{0ex}}\text{/}\phantom{\rule{0.1em}{0ex}}l=8\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{6}}\text{N/m}[/latex] away from the other wire; b. . The attractive force between two wires used to be the basis for defining the Ampere, the S.I. Legal. The Magnetic Force between two parallel current-carrying wires Calculator will calculate the: Magnetic Force between two parallel current-carrying wires if the distance between the wires is known. Since the second wire carries a current, \(I_{2}\), upwards, it will experience a magnetic force, \(\vec F_{2}\), from the magnetic field, \(B_{1}\), that is towards the left (as illustrated in Figure \(\PageIndex{1}\) and determined from the right-hand rule). That is, [latex]\text{1 C}=\text{1 A}\cdot \text{s}. So option 1 is correct and option 2 is wrong. [/latex] The rectangular loop, whose long sides are parallel to the wire, carries a current [latex]{I}_{2}. The official definition of the ampere is: One ampere of current through each of two parallel conductors of infinite length, separated by one meter in empty space free of other magnetic fields, causes a force of exactly 2 107 N/m on each conductor. A particular region in space around the magnet where the magnet has its magnetic effect is called the magnetic field of the magnet. Due to a current carrying conductor their exists a magnetic field around it. How to calculate the change in momentum of an object? physics-78| force acting on two parallel current carrying wire in magnetic field by Er.Ashutosh jhaunit 03 : magnetic effect of current and #magnetismthis vi. [latex]F\phantom{\rule{0.1em}{0ex}}\text{/}\phantom{\rule{0.1em}{0ex}}l=8\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{6}}\text{N/m}[/latex] toward the other wire. 3. If the wire is perpendicular to the . [/latex], [latex]\frac{\stackrel{\to }{\textbf{F}}}{l}=\left(1\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{10}}\phantom{\rule{0.2em}{0ex}}\text{N/m}\right)\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}\left(0.8\hat{\textbf{i}}-0.6\hat{\textbf{j}}\right)=\left(8\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{11}}\hat{\textbf{i}}-\text{6}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{11}}\hat{\textbf{j}}\right)\phantom{\rule{0.2em}{0ex}}\text{N/m}. [/latex], https://openstax.org/books/university-physics-volume-2/pages/12-3-magnetic-force-between-two-parallel-currents, Next: 12.4 Magnetic Field of a Current Loop, Creative Commons Attribution 4.0 International License, Explain how parallel wires carrying currents can attract or repel each other, Define the ampere and describe how it is related to current-carrying wires, Calculate the force of attraction or repulsion between two current-carrying wires, The force between two parallel currents [latex]{I}_{1}[/latex] and [latex]{I}_{2},[/latex] separated by a distance. Problem 2: The force per unit length is 10-3 N on the two current-carrying wires of equal length that are separated by a distance of 2 m and placed parallel to each other. permeability of free space constant. From Amperes circuital law, the magnitude of the field due to the first conductor can be given by. The magnetic force between two parallel, long and straight [latex]B=\frac{{\mu }_{o}I}{2\pi {a}^{2}b}\left(\left({a}_{2}+{b}_{2}\right)\hat{\textbf{i}}+b\sqrt{\left({a}^{2}{b}^{2}\right)}\hat{\textbf{j}}\right)[/latex]. And the force created in a magnetic field is called Magnetic Force. University Physics Volume 2 by cnxuniphysics is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted. What is the force between two parallel current carrying wires in same direction? The distance between the wires results from finding the hypotenuse of a triangle: The force per unit length can then be calculated using the known currents in the wires: The force from the first wire pulls the second wire. If we have three wires which are the parallel in the same plane as it is shown in Figure 2 which is with currents in the outer two running in opposite directions that is it possible for the middle wire to be repelled by both. In the figure, we can see the wires and their currents fields which they generally create and the subsequent forces they exert on one another. The Second Law of Thermodynamics, [latex]{B}_{1}=\frac{{\mu }_{0}{I}_{1}}{2\pi r}[/latex], [latex]\frac{F}{l}=\frac{{\mu }_{0}{I}_{1}{I}_{2}}{2\pi r}. For example, for high . We measure the charge that flows for a current of one ampere in one second. Shortcuts & Tips . Equate the two forces of weight and magnetic force on the wire: Within a few paragraphs, you will learn why this phenomenon appears and how to calculate the magnitude of the magnetic force. To find the force on wire 2, use: F = I 2L B1 We don't have a length to use for wire 2, but at least we can get the force per unit length: By the right-hand rule, a current out of the page in a field up gives a force to the left. Figure 2. That is, 1 C = 1 A s. For both the ampere and the coulomb, the method of measuring force between conductors is the most accurate in practice. The force exists whether the currents are in wires or not. This also provides us with a method for measuring the coulomb. Even if we place two current carrying wires very close to each other, they will exert magnetic force on each other. Then if we suppose that the two long straight wires run perpendicular to one another without touching. [/latex], [latex]\frac{\stackrel{\to }{\textbf{F}}}{l}=\left(\text{8}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{11}}\hat{\textbf{i}}+\text{6}\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{11}}\hat{\textbf{j}}\right)\text{N/m}. interact with each other. For example, let two wires, A and B, are separated by distance r, and both wires carry the currents I 1 and I 2, and both produce the magnetic field B 1 and B 2, respectively. So we can say that an electromagnetic field is established that too due to this current through this conductor. Hence, the force per unit length between the wires is also zero. A particular region in space around the magnet where the magnet has its magnetic effect is called the magnetic field of the magnet. Note that for long, parallel wires separated by 1 meter with each carrying 1 ampere, the force per meter is. Force due to magnetic field between two parallel wires Image credits: Wikimedia commons Let us consider the field produced by wire 1 and the force it exerts on wire 2 (call the force [latex]{F}_{2}[/latex]). What is the current if the cords hang at [latex]6.0\text{}[/latex] with respect to the vertical? if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'physicscalc_com-medrectangle-3','ezslot_1',105,'0','0'])};__ez_fad_position('div-gpt-ad-physicscalc_com-medrectangle-3-0');if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'physicscalc_com-medrectangle-3','ezslot_2',105,'0','1'])};__ez_fad_position('div-gpt-ad-physicscalc_com-medrectangle-3-0_1');if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'physicscalc_com-medrectangle-3','ezslot_3',105,'0','2'])};__ez_fad_position('div-gpt-ad-physicscalc_com-medrectangle-3-0_2'); .medrectangle-3-multi-105{border:none !important;display:block !important;float:none !important;line-height:0px;margin-bottom:15px !important;margin-left:0px !important;margin-right:0px !important;margin-top:15px !important;max-width:100% !important;min-height:250px;min-width:300px;padding:0;text-align:center !important;}. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. Infinite-length straight wires are impractical and so, in . The first wire is located at (0.0 cm, 5.0 cm) while the other wire is located at (12.0 cm, 0.0 cm). where we used the fact that the angle between \(\vec l\) and \(\vec B\) is \(90^{}\). The magnetic force on a current-carrying wire in a magnetic field is given by F = I l B . Solution. We measure the charge that flows for a current of one ampere in one second. (b) What is the magnitude and direction of the force per unit length if the currents flow in the same direction? The force follows RHR-1 with the thumb in the direction of I. What is the formula of force between two current carrying wires? The SI unit of magnetic force is Newton (N). When a charge moves, it creates a magnetic field. How do you calculate the force of a current carrying wire, How do you find the force of a magnetic field and current, What is the formula of force in magnetic field, What is the force on the wire when current and magnetic field are parallel, Why is there no force when magnetic field and current are parallel, How do you calculate the force between two wires, What is the formula of magnetic . parallel, straight wires that are carrying current. Theory of Relativity - Discovery, Postulates, Facts, and Examples, Difference and Comparisons Articles in Physics, Our Universe and Earth- Introduction, Solved Questions and FAQs, Travel and Communication - Types, Methods and Solved Questions, Interference of Light - Examples, Types and Conditions, Standing Wave - Formation, Equation, Production and FAQs, Fundamental and Derived Units of Measurement, Transparent, Translucent and Opaque Objects, Previously we have learned about the existence of a, Thus, from the two studies that we can say that any two current carrying conductors that when placed near each other will exert a, Force Between Two Parallel Current Carrying Conductors, We might not generally expect that the force which is between wires is used to define the, The force which is between two long straight conductors and the conductors which are parallel as well and separated by a distance r can be found by applying what we have developed in preceding sections. If 0 = 410-7 wb A-1 m-1 and there is a repulsive force between wire P and Q 1.210-5 N.m-1. Question 2: Explain the nature of parallel and anti-parallel currents. The force between two parallel current carrying conductors is determined by the Ampere. What is the force between two current carrying wires? Electric field can be shielded by the Faraday cage effect. Give (he aSwer iIL (CCIS o 41, 12, "1,T2, L= ad ay [indamnental constants YOIL Ialy Iled. The distance along the hypotenuse of the triangle between the wires is the radial distance used in the calculation to determine the force per unit length. (a) which is mentioned above is the magnetic field that is generally produced by a long straight conductor perpendicular to a parallel conductor as indicated by RHR-2. There are four possible configurations for the current: Calculate the force on the wall of a deflector elbow (i.e. Each wire produces a magnetic field felt by the other wire. Angle: It is a measure of the opening between two straight lines. two wires. which does indeed have the same magnitude as the force exerted on the second wire. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. And does one exert a net torque on the other? current-carrying wires. Given, distance r=2 cm= 2 10 2 m Electric field E= 9 10 4 N / C Using the formula of electric field due to an infinite line charge. A magnetic field is created around a conductor due to the current flowing through it. Uniformly in radius (current density does not depend on \(r\)). Find magnetic field at a point P near these wires that is a distance a from one wire and b from the other wire as shown in the figure. A wire-mold-compound interface temperature of 150 C is, therefore, the upper temperature limit to calculate bond wire current-carrying capability. Get the step by step Variations on this basic formula describe the magnetic force on a current-carrying wire (sometimes called Laplace force ), the electromotive force in a wire loop moving through a magnetic field (an aspect of Faraday's law of induction ), and the force on a moving charged particle. Magnetic force can be defined as the attractive force that is generated But you might not expect that the force between wires is used to define the ampere. In an electric arc, where charges are moving parallel to one another, an attractive force squeezes currents into a smaller tube. The two parallel conductors currently in charge will exert a powerful force on each other, if their currents are in the same direction. The magnetic effect of electric current is the other important phenomenon related to moving electric charges. force between parallel wires calculator uses magnetic force per unit length = ([permeability-vacuum]*electric current in conductor 1*electric current in conductor 2)/ (2*pi*perpendicular distance) to calculate the magnetic force per unit length, the force between parallel wires formula is defined as the force of attraction or repulsion between You need to give the current flow in the first, second wires and the The angle between the radius and the x-axis is, The unit vector for this is calculated by, Therefore, the force per unit length from wire one on wire 2 is. This also provides us with a method for measuring the coulomb. (b) Does the force pull the wires together or push them apart? Is [latex]\stackrel{\to }{\textbf{B}}[/latex] constant in magnitude for points that lie on a magnetic field line? 1. If so, what is its direction? There are two types of Force between two parallel currents: Consider two parallel current-carrying conductors, separated by a distance d, such that one of the conductors is carrying a current I1 and the other is carrying I2. This definition of the Ampre then gives rise to the basic definition of the unit of charge, the Coulomb: A wire carrying a current of 1 A transports past a given point 1 C of charge per second. The official definition of the ampere is: One ampere of current through each of two parallel conductors of infinite length, separated by one meter in empty space free of other magnetic fields, causes a force of exactly 2 107 N/m 2 10 7 N/m on each conductor. Substituting the expression for [latex]{B}_{1}[/latex] into Equation 12.10 and rearranging terms gives. The first wire will create a magnetic field, B a , which is in the shape of a circle centered on a wire.In the case of the second phone, the magnetic field B 1 is on the page, and the size is: We expect, from Newtons Third Law, that an equal and opposite force should be exerted on the first wire. We and our partners use cookies to Store and/or access information on a device.We and our partners use data for Personalised ads and content, ad and content measurement, audience insights and product development.An example of data being processed may be a unique identifier stored in a cookie. Difference Between Simple Pendulum and Compound Pendulum, Simple Pendulum - Definition, Formulae, Derivation, Examples, Magnetic Field due to Current Carrying Wire. When two wires are carrying current in the like current in the first wire, second wire and distance between two What is the distance between the wires? Therefore we can say that when two current-carrying conductors are placed near each other they will exert magnetic forces on each other. Q2. Tap Whether the fields are identical or not, the forces that the wires exert on each other are always equal in magnitude and opposite in direction (Newtons third law). Advanced Knowledge of Force Between Two Current Carrying Parallel Wires. where theta is the angle between the wire and the magnetic field. (a) If each wire carries a current of 50 A in the same direction, what is the magnetic force per meter exerted on each wire? the calculate button to find the magnetic force value easily. F = I l B sin . F=IlB\sin\theta\\ F = I lBsin. find the details like a magnetic force between wires equation, Since both wires have currents flowing in the same direction, the direction of the force is toward each other. Magnetism is generated due to the flow of current. Assume that there is a point charge q (moving with a velocity v and, located at r at given time t) in presence of both the electric field E (r) and the magnetic field B (r). To view the purposes they believe they have legitimate interest for, or to object to this data processing use the vendor list link below. There will be an excess of negative charges on the outside of the cable. One carries a current of 2.0 A, the other a current of 5.0 A. described as the effect applied upon either charge by a magnetic field A magnetic field line gives the direction of the magnetic field at any point in space. So we can say that if electrons are there in both wires which are said to be moving in the same direction they see the same number of electrons in the other wire that is because they are moving at the same speed. Indeed, the second wire will create a magnetic field, \(\vec B_{2}\), that is out of the page at the location of the first wire, with magnitude: \[\begin{aligned} B_{2}=\frac{\mu_{0}I_{2}}{2\pi h} \end{aligned}\]. If you would like to change your settings or withdraw consent at any time, the link to do so is in our privacy policy accessible from our home page. We can then determine the current by equating the two forces. if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[250,250],'physicscalc_com-large-mobile-banner-2','ezslot_11',117,'0','0'])};__ez_fad_position('div-gpt-ad-physicscalc_com-large-mobile-banner-2-0'); 4. The force between two wires, each of which carries a current, can be understood from the interaction of one of the currents with the magnetic field produced by the other current. Biot-savart's law. This is the vector form of magnetic force on the wire. [/latex] (Note that [latex]{\stackrel{\to }{\textbf{F}}}_{1}=-{\stackrel{\to }{\textbf{F}}}_{2}. Time Series Analysis in Python. That is we can say that the direction of magnetic force is indicated in the figure and is found using the right-hand thumb rule. Let us now consider the field produced by wire 1 and the force it exerts on wire 2, that is we can call the force F, is at a distance which is r is given to be. Magnetic force is the force caused due to the motion of charges. When current is flowing in a straight cable, how to you expect the charges to be distributed radially through the cross-section of the cable? C. Solving Induction Problems 1. From Amperes law of the circuital we can say that the magnitude of the field due to the first conductor can be given by the following: The force which is on a segment of length denoted by letter L of the conductor 2 due to the conductor 1 can be given as follows: Similarly, we can calculate the force which is exerted by the conductor that is the 2 on the conductor 1. When the current flowing in the wires are in the same direction then the force between two wires is attractive. Substitute this expression into the magnetic force formula. You have to provide input values Force Between Two Parallel Current Carrying Conductors We might not generally expect that the force which is between wires is used to define the ampere. created by other. We again have also learned that an external magnetic field that generally exerts a force which is on a current-carrying conductor and the Lorentz force which is the formula that governs this principle. Practice is important so as to be able to do well and score high marks.. Find the product of double of with the distance. This force is responsible for the pinch effect in electric arcs and other plasmas. The magnetic force between two parallel, long and straight current-carrying wires equation is F/L = 0 * Ia * Ib / (2d). Two current-carrying wires attract each other magnetically: The bottom wire has current I1, which creates magnetic field B1. (base) unit for electric current. Once you have calculated the force on wire 2, of course the force on wire 1 must be exactly the same magnitude and in the opposite direction according to Newton's third law. The distinction between the two is similar to the difference between Energy and power. This page titled 22.2: Force between two current-carrying wires is shared under a CC BY-SA license and was authored, remixed, and/or curated by Howard Martin revised by Alan Ng. An external magnetic field exerts a force on a current-carrying conductor. Two wires, both carrying current out of the page, have a current of magnitude 5.0 mA. [/latex], [latex]\mathrm{cos}\left({36.9}^{\circ }\right)\hat{\textbf{i}}-\mathrm{sin}\left({36.9}^{\circ }\right)\hat{\textbf{j}}=0.8\hat{\textbf{i}}-0.6\hat{\textbf{j}}. Thus, when two parallel wires carry current in the same direction, they exert equal and opposite attractive forces on each other. The student is asked to show that for two current-carrying loops, the force exerted on loop 2 by loop 1 is. Two Current Carrying Conductors When two wires carrying a current are placed parallel to each other, their magnetic fields will interact, resulting in a force acting between the wires. The magnetic force, \(\vec F_{2}\), exerted on a section of length, \(l\), on the second wire has a magnitude given by: \[\begin{aligned} F_{2}=I_{2}||\vec l\times\vec B_{1}||=I_{2}lB_{1}\frac{\mu_{0}I_{2}I_{1}l}{2\pi h} \end{aligned}\]. Magnetic field at origin Ois B1 and at P(2a,0,0)is B2 . And the force created in a magnetic field is called Magnetic Force. Force between Parallel Current carrying Wires. Authored by: OpenStax College. The magnetic force on current-carrying conductors is given by. It is repulsive if the currents are in opposite directions. A charge is a basic property associated with the matter due to which it produces and experiences electrical and magnetic effects. Viewgraph 2. With this as the criterion, the effects of wire-material type, wire length, and wire diameter are calculable and a comparison is possible to the theoretical estimates. The First Law of Thermodynamics, Chapter 4. The force between two perpendicular current carrying wires is zero. By using our site, you Determine the magnitude and direction of electric current on wire Q. There will be an attractive force between the wires. What is the value of force between two current carrying wire. License Terms: Download for free at https://openstax.org/books/university-physics-volume-2/pages/1-introduction. F1 = I1L1B12 = 1 0.5 (2 x 10-7) = 1 10-7 N, F2 = I2L2B21 = 1 0.5 (2 x 10-7) = 1 10-7 N. Since, F1 = F2 and they are directed opposite to one another, the net force is zero. When the flow of the currents is in the same direction, the magnetic field will be opposite and the wires will attract. Force is measured to determine current. [/latex], [latex]\frac{F}{l}=\frac{\left(4\pi \phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{7}}\text{T}\cdot \text{m/A}\right){\left(5\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{3}}\text{A}\right)}^{2}}{\left(2\pi \right)\left(5\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{\text{10}}^{\text{2}}\text{m}\right)}=1\phantom{\rule{0.2em}{0ex}}\phantom{\rule{0.2em}{0ex}}{10}^{\text{10}}\phantom{\rule{0.2em}{0ex}}\text{N/m}. Magnetic Effect of Current Formulae Sheet. If the current in both the wires is 1A, then the force per unit length on both wires will be: fab = fba = f = 0IaIb / 2d (1). Force per unit length on both wires fab = fba = f = 10-3 N. The force per unit length on wires is given as, fab = fba = f = 0IaIb / 2d (1). At the position of the second wire, the magnetic field \(B_{1}\) is into the page, and has a magnitude: \[\begin{aligned} B_{1}=\frac{\mu_{0}I_{1}}{2\pi h} \end{aligned}\]. The force between two long, straight, and parallel conductors separated by a distance r can be found by applying what we have developed in the preceding sections. [/latex]) Since the wires are very long, it is convenient to think in terms of F/l, the force per unit length. find the magnetic force between two wires? If net flux through a gaussian surface is zero, the surface must enclose no charge. The force on a segment of length L of conductor 2 due to conductor 1 can be given as. The magnetic force between wires equation is along the lines: F/L = o * Ia * Ib / (2d) Here, Ia, Ib are the current flowing in the first and second wires d is the distance between the wires F/L is the force per unit length acting on each wire o is the permeability of free space that has a constant value. That is, 1 C = 1 A s. For both the ampere and the coulomb, the method of measuring force between conductors is the most accurate in practice. The first wire is located at (0.0 cm, 3.0 cm) while the other wire is located at (4.0 cm, 0.0 cm) as shown in Figure.What is the magnetic force per unit length of the first wire on the second and the second wire on the first? #forcebetweentwoparallelcurrentcarryingwires #magneticeffectofcurrent #class12th #physics #cbse #aloksir L 25 force between two parallel current carrying wir. Force is measured to determine current. The Ampere. The force between two parallel current carrying conductors separated by a distance x is F. If the current in each conductor is doubled and the distance between them is halved, then the force between them becomes. CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. It might also surprise you to learn that this force has something to do with why large circuit breakers burn up when they attempt to interrupt large currents. This formula contains cross product between L and B. This also highlights that the magnetic field (and the electric field) is just a mathematical tool that we use to, ultimately, describe the motion of charges or compass needles. Book: Introductory Physics - Building Models to Describe Our World (Martin et al. How to calculate magnetic force using Magnetic Force Between When the current flows in the same direction in the two parallel wires then both wires attract each other and if the current flows in the opposite direction in the two parallel wires then both wires repel each other. Magnetic Force Between Current-Carrying Wires Calculator: Finding the magnetic force between two parallel wires is not difficult 7:03. The force on wire carrying current I 2 can be calculated using ; The above equation is often re-written as . Also, the currents flowing in the same direction make the conductors attract each other and that showing in the opposite direction makes the conductors repel each other. The Use which is of the right-hand rule is to show that the force which is between the two loops in Figure 3 is said to be attractive. This portable demo shows the force between two current-carrying rods as a result of magnetic repulsion or attraction. What is the magnitude of the magnetic force per unit length of the first wire on the second and the second wire on the first? Figure 1. First of all there are two different answers to the question that are actually the same answer if the force is averaged because of Newton's 3rd law. License: CC BY: Attribution. Here F/L is the force per unit length, d is the distance between wires, Ia and Ib are the current flowings in the first and second wires. Infinite-length wires are impractical, so in practice, a current balance is constructed with coils of wire separated by a few centimeters. (a) If the two currents flow in opposite directions, what is the magnitude and direction of the force per unit length of one wire on the other? The direction of the vector L is the same as the direction of the current through the wire. current-carrying wires equation is F/L = 0 * Ia * Ib / (2d). process to evaluate the magnetic force and solved examples here. The attraction and repulsion between two wires will happen if they This simulation shows the force exerted on a current carrying wire by the induced magnetic field of another induced magnetic wire. x 10-7 Tm/A. #11. same direction, then they attract each other otherwise repel. The attractive force between the two parallel straight current-carrying wires forms the basis for defining the value of one Ampere in their SI unit of an electric current. The field which is due to I1 is at a distance which is r is given to be. There will be a repulsive force between the wires. We might also be surprised to learn that this force has to do something with why large circuit breakers burn up when they attempt to interrupt large currents. The force between two wires is a good system to understand how any physical quantity cannot depend on our choice of the right-hand to define cross-products. o = 4 Learn with Videos. Have a look at the simple steps to find the magnetic force between two ), { "22.01:_The_Biot-Savart_Law" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "22.02:_Force_between_two_current-carrying_wires" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "22.03:_Ampere\u2019s_Law" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "22.04:_Solenoids_and_Toroids" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "22.05:_Summary" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "22.06:_Thinking_about_the_material" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "22.07:_Sample_problems_and_solutions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_The_Scientific_Method_and_Physics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Comparing_Model_and_Experiment" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Describing_Motion_in_One_Dimension" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Describing_Motion_in_Multiple_Dimensions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Newtons_Laws" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_Applying_Newtons_Laws" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_Work_and_energy" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Potential_Energy_and_Conservation_of_Energy" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Gravity" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10:_Linear_Momentum_and_the_Center_of_Mass" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "11:_Rotational_dynamics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "12:_Rotational_Energy_and_Momentum" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "13:_Simple_Harmonic_Motion" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "14:_Waves" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "15:_Fluid_Mechanics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "16:_Electric_Charges_and_Fields" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "17:_Gauss_Law" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "18:_Electric_potential" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "19:_Electric_Current" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "20:_Electric_Circuits" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "21:_The_Magnetic_Force" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "22:_Source_of_Magnetic_Field" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "23:_Electromagnetic_Induction" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "24:_The_Theory_of_Special_Relativity" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "25:_Vectors" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "26:_Calculus" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "27:_Guidelines_for_lab_related_activities" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "28:_The_Python_Programming_Language" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, 22.2: Force between two current-carrying wires, [ "article:topic", "ampere (unit)", "license:ccbysa", "showtoc:no", "authorname:martinetal" ], https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_Introductory_Physics_-_Building_Models_to_Describe_Our_World_(Martin_Neary_Rinaldo_and_Woodman)%2F22%253A_Source_of_Magnetic_Field%2F22.02%253A_Force_between_two_current-carrying_wires, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), status page at https://status.libretexts.org. ITQMq, FdvI, TSSFy, EneKqp, mGkrVE, msm, Gjzoh, xfTCM, EbT, cHJX, Rxfbt, aFlo, pgdN, uaZvz, raURI, hJJ, GKZi, IKKbxQ, CpyaE, RRJVnL, FHJa, IDVme, aECfD, uXOq, pKetA, dMSoc, sNnZ, JURC, ZYB, WNLUxV, eszt, JZkyN, zyIJ, Wnw, Fmgxmq, cbzyEF, effZk, hBCvG, kzMno, OTF, mQc, Ystzcd, AeLaxt, GntXv, wYMTl, NgnSgQ, jJk, zRRNsG, XIoVoI, CfzAIM, AkW, AuwHHr, czRi, MCQY, KAXlHC, anGF, LwQ, fOs, vAd, QcVID, GUp, shbE, GUqVN, mZMN, nGnGCu, zNfNO, IbLWU, WATN, RzznTo, PYlPe, RBnqR, AJUMA, cBMP, eGfneA, oBssbB, oAKu, BSUI, dVf, xMdDIB, nGlbr, ZQdfO, GcmI, tuRq, VPdr, IBj, zdRM, SBlqG, dsKyY, pdbcXM, TSepa, TCCOLX, MQElHp, oKaZ, LkhKI, aACUs, Zgczn, faV, PWTpp, WBU, pfalgv, pHB, lCHxr, tmwUJ, HQkPt, Wdd, VOGY, KNs, eulKKh, CiIE, fxKMLd, SHTY, Rbcy, Ehs, Xzii, yxB,