a) A single transmission line is 40m above the surface of the Earth and carries

Question

a) A single transmission line is 40m above the surface of the Earth and carries 2000A of curent. What is the peak magnetic field at ground level directly under the wire?

b) Suppose now that we have a two wire system in which the currents are opposite in direction at the same height. Assume that the maximum current from part (a) is flowing in each wire. Suppose the wires are separated horizontally by 4m.

What is the magnetic field at a point on the surface of the Earth directly under the midpoint between the two wires?

*You need to use vectors for this part but only focus on the y components

Explanation / Answer

Part A)

The magnetic field from a wire if found by the formula

B = oI/2r

B = (4 X 10-7)(2000)/(2)(40)

B = 1 X 10-5 T

Part B)

When we have two wires, and we are looking at the point midway between them, the r is a little larger than 40. The r = 40.05m, so the new magnetic field from each wire at that point is 9.99 X 10-6 T

The x components of the field at that point will cancel out due to the fact that the currents in the wires are going in the opposite directions. However, there will be y components of the field that will add, and point in the upward direction.

The total y component is...

(2)(9.99 X 10-6)(sin 2.86) = 9.97 X 10-7 T directed upward

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