Two short bar magnets P and Q are arranged such that their centers are on the X-axis and are separated by a large distance. The magnetic axes of P and Q are along the X and Y axes respectively. At a point R, midway between their centers, if B is the magnitude of induction due to Q, the magnitude of total induction at R due to both magnets is

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$\sqrt{5} B$

$\frac{\sqrt{5}}{2} B$

answer is B.

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Detailed Solution

$B_{R} = \sqrt{{B^{2}}_{P}} + \sqrt{{B^{2}}_{Q}} = {\sqrt{(\frac{μ_{\circ}}{4 π} \frac{2 M}{d^{3}})}}^{2} + {\sqrt{(\frac{μ_{\circ}}{4 π} \frac{M}{d^{3}})}}^{2} \sqrt{5} \frac{μ_{\circ}}{4 π} \frac{M}{d^{3}} = \sqrt{5} B \{B_{Q} = \frac{μ_{0} M}{4 π d^{3}} = B\}$

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