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Due to currents in infinite long wires at A and B, magnetic field is zero at the mid-point of AB and direction of magnetic field at P is as shown in figure. Then

I. The current is equal in both wires and inside the plane of paper
II. The magnetic field left of O is upward
III. The magnetic field is maximum at $x = \pm d$

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I, II

II, III

I, III

I, II, III

answer is D.

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Detailed Solution

Question Image
$B_{P} = B = 2 B_{0} \cos θ = 2 \cdot \frac{μ_{0} I}{2 π \sqrt{d^{2} + x^{2}}} \cdot \frac{x}{\sqrt{d^{2} + x^{2}}} = \frac{μ_{0} I x}{d^{2} + x^{2}}$
$\frac{d B}{d x} = (d^{2} + x^{2}) \cdot 1 - x (0 + 2 x) = 0$
$x = \pm d$

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