Two identical short bar magnets each having magnetic moment M are...

Two identical short bar magnets each having magnetic moment

M

are placed at a distance of

2d

with their axes perpendicular& to each other in a horizontal plane. The magnetic induction at a point midway between them is Two identical short bar magnets each having magnetic moment M are placed at a distance of 2d with their axes

Two identical short bar magnets each having magnetic moment M are placed at a distance of 2d with their axes

Options

A $\dfrac{\sqrt{2}{μ}_{0}M}{4\pid^{3}}$
B $\dfrac{\sqrt{3}{μ}_{0}M}{4\pid^{3}}$
C $\dfrac{{μ}_{0}M}{2\pid^{3}}$
D $\dfrac{\sqrt{5}{μ}_{0}M}{4\pid^{3}}$

Correct answer

D. $\dfrac{\sqrt{5}{μ}_{0}M}{4\pid^{3}}$

Step-by-step solution

At

magnetic field is a vector quantity. at point p two magnetic field are acting at 90^o

{B}_{net} = \sqrt{{B}_{1}^{2} + {B}_{2}^{2}}

= \sqrt{\left(\dfrac{2{μ}_{0}M}{4{\pid}^{3}}\right)^{2} + \left(\dfrac{{μ}_{0}M}{4{\pid}^{3}}\right)^{2}} = \dfrac{{μ}_{0}M}{4{\pid}^{3}} \left(\sqrt{5}\right)

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