Straight wires and magnetic fields?

Question

Simple question I think but I can't seem to grasp it. Can you help?

The magnetic field of the Earth is approximately 0.5 ×10−4 T. What current in a long straight wire would produce a field of equal strength at a distance of 5 cm from the wire?

Answer 1

Suppose current is i.

Distance of point from the wire r = 5 cm = 0.05 m

Magnetic field B = (µ0/2π)*(i/r)

µ0 = 4π * 10^-7

Therefore, µ0/2π = 2 * 10^-7

Therefore, B = 2 * 10^-7 * i/0.05 = 4 * 10^-6 * i

From problem,

4 * 10^-6 * i = 0.5 * 10^-4

Or, i = (0.5 * 10^-4)/(4 * 10^-6)

= (0.5/4)*(10^-4/10^-6)

= 0.5/4 * 100

=50/4 = 12.5 ampere

Ans: 12.5 ampere

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