9. Magnetic Force between Two Wires

Experiment 9: Magnetic Force between Two Wires Theory The magnetic field of an infinitely long straight wire carrying the current I at distance r from the wire is: B = μ 0 I 2 πr (1) where μ 0 = 4 π× 10 − 7 T ∙m / A . Magnetic field B exerts force F on the straight wire of length l carrying the current I placed into this magnetic field F = IlBsinθ (2) where θ is an angle between I and B . It follows from this theory that if two wires with currents are placed next to each other the wire 1 will exert force on wire 2 and vice versa. Figure 1 shows two parallel long wires separated by distance r and carrying the currents I 1 and I 2 , and the magnetic fields they create (only magnetic field produced by wire 1 is shown). Magnetic field B 1 produced by wire 1 exerts force F 2 on wire 2. The field B 1 due to I 1 at a distance r is given by Eq. (1) Figure 1 This field is uniform along wire 2 and perpendicular to it. Therefore, the force F 2 it exerts on wire 2 is given by Eq. (2) where θ = 90 ° Combining Eqs. (1) and (2) we obtain the magnetic force F 2 per unit wire length as F 2 l = μ 0 I 1 I 2 2 πr (3) By Newton’s third law, the same force but in opposite direction is exerted on wire 1 by the wire 2

F 1 =− F 2 so that parallel currents attract each other. Similar calculation shows that anti-parallel currents repel each other. The goal of this lab is to check Equation (3) experimentally by measuring the magnetic force between two parallel current-carrying wires. Procedure Physics Simulations: Forces Between Two Current-Carrying Wires https://www.geogebra.org/m/JSrCbknr Part A. Magnetic force vs distance between the wires 1. Set the current in wire A = 3 Amp, the current in wire B = 5 Amp and initial distance between the wires = 2m 2. Measure the force between the wires as you increase the distance by 0.5 meters and record your data in the data table 3. Calculate the force using Eq. (3) and record your results in the data table. distance 2 m 2.5 m 3 m 3.5 m 4 m 4.5 m Force , exp. 15*10^-7 12*10^-7 10*10^-7 8.57*10^-7 7.5*10^-7 6.67*10^-7 Force , theor. 15*10^-7 12*10^-7 10*10^-7 8.57*10^-7 7.5*10^-7 6.67*10^-7 Part B. Magnetic force vs current 1. Set the current in wire A = 3 Amp, the distance between the wires = 2m and initial current in wire B = 3A 2. Measure the force between the wires as you decrease the current in wire B by 1 A and record your data in the data table. 3. Calculate the force using Eq. (3) and record your results in the data table. Wire B ( Amp ) 3 A 2 A 1 A 0 A − 1 A − 2 A Force , exp. 9*10^-7 6*10^-7 3*10^-7 0*10^-7 3*10^-7 6*10^-7 Force , theor. 9*10^-7 6*10^-7 3*10^-7 0*10^-7 -3*10^-7 -6*10^-7