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Question

# Two parallel long wires carry currents i1 & i2 (i1> i2) when the currents are in the same direction. The magnetic induction at a point midway between the two wires is X. If the direction of i2 is reversed, the magnetic induction becomes 2X, then i1/ i2 is:

A
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B
2
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C
3
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D
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Solution

## The correct option is B 3At midway point when current is in same directionB=μ0i12πr+μ0(−i2)2πr=μ02πr(i1−i2)=XAt midway point when current is in opposite directionB=μ0i12πr+μ0(i2)2πr=μ02πr(i1+i2)=2XSo, μ02πr(i1+i2)μ02πr(i1−i2)=2XX⇒i1+i2i1−i2=2⇒i1i2=3

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