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Let two long parallel wires a distance ‘d’ apart, carry equal current ‘i’ in the same direction. One wire is at x=0, the other at x=d. Determine magnetic field at any point on x-axis between the wires as a function of ‘x’.

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a

B=μ0i(d−2x)2πx(d−x)j^

b

B=μ0i(2x−d)2πd(d−x)i^

c

B=μ0i(x−2d)πx(d−x)k^

d

B=μ0i2πd2x−dd−x−j^

answer is A.

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Detailed Solution

Let us consider a point ‘P’ at a distance (x,y) from the wire 1. 0≤x≤dHence B→1=μ0i2πxj^The point is at a distance d−x from wire 2. ∴ B→2=−μ0i2π(d−x)j^ ∴ B→net=B→1+B→2=μ0i2πxj^−μ0i2π(d−x)j^B→net=μ0i(d−2x)2πx(d−x)j^ .

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Let two long parallel wires a distance ‘d’ apart, carry equal current ‘i’ in the same direction. One wire is at x=0, the other at x=d. Determine magnetic field at any point on x-axis between the wires as a function of ‘x’.