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

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 $$B_2 = \dfrac { \mu_0}{ 4 \pi}. \dfrac {M}{d^3}$$$$\Rightarrow B_{net} = \dfrac { \mu_0}{ 4 \pi }. \dfrac { \sqrt {5} M }{d^3}$$Physics

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