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Two infinitely long conducting wires carry currents, as shown in figure. If the horizontal wire carrying current produces a magnetic field $B$ at the point $P (- d, - 2 d)$ then the resultant magnetic field at this point is

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$- 2 B \hat{k}$

zero

$\sqrt{2} B \hat{k}$

$- \sqrt{2} B \hat{k}$

answer is A.

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Detailed Solution

Given $B = \frac{μ_{0}}{2 π} \cdot \frac{(2)}{d}$ .

Magnetic field due to $4 A$ wire, $B' = \frac{μ_{0}}{2 π} \frac{(4)}{2 d} = B$ .

So, resultant magnetic field $= B + B = 2 B$ along $- v e z - a x i s$ .

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