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Question

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


A
μ04π(2)Md3
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B
μ04π(3)Md3
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C
(2μ0π)Md3
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D
μ04π(5)Md3
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Solution

The correct option is D $$\dfrac { { \mu }_{ 0 } }{ 4\pi } \left( \sqrt { 5 } \right) \dfrac { M }{ { d }^{ 3 } } $$
At point $$ P $$ net magnetic field $$ B_{net} = \sqrt { B^2_1 + B^2_2 } $$
Where $$ B_1 = \dfrac { \mu_0}{ 4 \pi} . \dfrac {2 M}{ d^3} $$ and $$ B_2 = \dfrac { \mu_0}{ 4 \pi}. \dfrac {M}{d^3} $$

$$ \Rightarrow B_{net} = \dfrac { \mu_0}{ 4 \pi }. \dfrac { \sqrt {5} M }{d^3} $$

1737738_1301875_ans_ec4815a490e642bdb59c31a78ad296bb.png

Physics

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