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Two long parallel wires carry equal current i flowing in the same direction are at a distance 2d apart. The magnetic field B at a point lying on the perpendicular line joining the wires and at a distance x from the mid-point is

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a

$\frac{μ_{0} i x}{π (d^{2} - x^{2})}$

b

$\frac{μ_{0} i x}{π (d^{2} + x^{2})}$

c

$\frac{μ_{0} i d}{π (d^{2} - x^{2})}$

d

$E Q \frac{μ_{0} i d}{π (d^{2} + x^{2})}$

answer is B.

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Detailed Solution

Question Image

The magnetic field due to first wire
$B_{1} = \frac{μ_{0} i}{2 π (d + x)}$
Due to second wire
$B_{2} = \frac{μ_{0} i}{2 π (d - x)}$
Both the magnetic fields act in opposite direction.
$B = B_{2} - B_{1} = \frac{μ_{0} i}{2 π} (\frac{1}{d - x} - \frac{1}{d + x}) = \frac{μ_{0} i x}{π (d^{2} - x^{2})}$

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