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= μ0I2πr                                                                              (1)   where μ0=4π×10-7T?m/A

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= μ0I2πr

                                                                             (1)

where μ0=4π×10-7T?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= Il Bsinθ

                                                                       (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 I1

 and I2

, and the magnetic fields they create (only magnetic field produced by wire 1 is shown). Magnetic field B1

  produced by wire 1 exerts force F2

 on wire 2. The field B1

 due to I1

 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 F2

 it exerts on wire 2 is given by Eq. (2) where θ=90°

Combining Eqs. (1) and (2) we obtain the magnetic force F2

 per unit wire length as

                                                                                     F2l= μ0I1I22πr

                                                                            (3)

By Newton’s third law, the same force but in opposite direction is exerted on wire 1 by the wire 2

F1=-F2

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.
Force , theor.

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.
Force , theor.

Questions

1. Based on your data in Part A how the magnetic force between two parallel currents depends on the distance between them?

2. Based on your data in Part B how the magnitude and direction of the magnetic force between two parallel currents depends on the direction and magnitude of the currents in the wires?