Assume that Earth’s magnetic field runs parallel to the surface of the ground from south to north with a magnitude of 0.50×10−4 T and that the supporting poles are 35 m apart.

Question

1) Find the magnitude of the force that Earth’s magnetic field exerts on a 35-m segment of wire carrying 75 A if the current runs from north to south

2) Find the magnitude and direction of the force that Earth’s magnetic field exerts on a 35-m segment of wire carrying 75 A if the current runs from east to west.

3)Find the magnitude and direction of the force that Earth’s magnetic field exerts on a 35 m segment of wire carrying 75 A if the current runs toward the northeast making an angle of 30∘ north of east.

Answer 1

The formula for this questions is F = ILBsinθ

1. if the wire runs N to S, then the angle with the magnetic field is 0, and sin0 is 0, and 0 times the other parameters is 0.
2. if the wire runs E to W, then the angle is 90. sin90 is 1, so the force F is ILB = 75 * 35 * 0.5x10^-4
3. if the wire is 30º north of east, then the angle between the wire and the magnetic field (running S to N) is 60º. sin60 is 0.866, so the force F = 75*35*0.5x10^-4 * 0.866