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Question

A straight, how wire carries a current of 20 A. Another wire carrying equal current is placed parallel to it. If the force acting on a length of 10 cm of the second wire is 2.0 × 10−5 N, what is the separation between them?

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Solution

Given:
Magnitude of current in both wires, i1 = i2 = 20 A
Force acting on 0.1 m of the second wire, F = 2.0 × 10−5 N
∴ Force per unit length = 2×10-50.1 = 2.0 × 10−4 N/m
Now,
Let the separation between the two wires be d.
Thus, the force per unit length is given by
Fl=μ0i1i22πd2.0×10-4=2×10-7×20×20dd=0.4 m=40 cm

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