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

<img alt="" src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fquizrr%252Fquestion-assets%252F99_percentile_module%252Ffinal-question%252Fimage14-c1fec844-baa1-4a3e-a03a-4fe4b7171672.jpg%3Falt%3Dmedia&clean=1&v=qxfig138"/ data-qx-orig-src="/assets/diagrams/qx-book-c3f21f64a533104a.png" data-qx-storage-src="/assets/diagrams/qx-book-c3f21f64a533104a.png">At<br/><br/>magnetic field is a vector quantity. at point p two magnetic field are acting at 90<sup>o</sup><br/><br/>

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

<br/><br/>

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

2 + \left(\dfrac{{μ}_{0}M}{4{πd}^{3}}\right)

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

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