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Question

Two parallel long wires carry currents i1 and i2 (i1 > i2). When the currents are in the same direction, the magnetic induction at a point midway between the wires is 10 μT. If the direction of i2 is reversed, the induction becomes 30 μT. The ratio of i1i2is :

A
4
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B
3
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C
2
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D
1
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Solution

The correct option is D 2
1st case:
B=B1B2
10×103=μ0i12πrμ0i22πr
μ02πr(i1i2)=0.01

2nd case:
B=B1+B2
30×103=μ0i12πr+μ0i22πr
μ02πr(i1+i2)=0.03
i1i2i1+i2=3
i1i2=3i1+3i2
i1i2=2

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