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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 :

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Solution

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1st case:

B=B1−B2

10×10−3=μ0i12πr−μ0i22πr

μ02πr(i1−i2)=0.01

2nd case:

B=B1+B2

30×10−3=μ0i12πr+μ0i22πr

μ02πr(i1+i2)=0.03

∴i1−i2i1+i2=3

i1−i2=3i1+3i2

i1i2=2

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