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Question

Current I1 and I2 flow in the wires as shown in the figure. The field is zero at a distance x to the right of O. Then,

A
x=(I1I2)a
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B
x=(I2I1)a
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C
x=(I1I2I2+I2)a
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D
x=(I1+I2I1I2)
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Solution

The correct option is C x=(I1I2I2+I2)a
Let's take a point P from point O at x distance where magnetic field is zero.

Magnetic filed due to element AB and element DE will be zero as point lie on the same axis as these elements.
Magnetic field due to element BC and DF will be in opposite direction and they must be equal so that net magnetic field at point P is zero.
B1=B2
We know that magnetic field due to semi infinite wire is
B=μ0I4πr

μ0I14π(a+x)=μ0I24π(ax)

axa+x=I2I1

x=(I1I2)(I1+I2)a

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