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Question: Two identical short bar magnets, each having magnetic moment of 10 Am<sup>2</sup>, are arranged such...

Two identical short bar magnets, each having magnetic moment of 10 Am2, are arranged such that their axial lines are perpendicular to each other and their centres be along the same straight line in a horizontal plane. If the distance between their centres is 0.2 m, the resultant magnetic induction at a point midway between them is

(μ0=4π×10−7Hm−1)\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm { Hm } ^ { - 1 } \right)

A

2×10−7\sqrt { 2 } \times 10 ^ { - 7 } Tesla

B

5×10−7\sqrt { 5 } \times 10 ^ { - 7 } Tesla

C

2×10−3\sqrt { 2 } \times 10 ^ { - 3 } Tesla

D

5×10−3\sqrt { 5 } \times 10 ^ { - 3 } Tesla

Answer

5×10−3\sqrt { 5 } \times 10 ^ { - 3 } Tesla

Explanation

Solution

From figure

=(μ04π⋅2Md3)2+(μ04π⋅Md3)2= \sqrt { \left( \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { 2 M } { d ^ { 3 } } \right) ^ { 2 } + \left( \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { M } { d ^ { 3 } } \right) ^ { 2 } }

=5⋅μ04π⋅Md3= \sqrt { 5 } \cdot \frac { \mu _ { 0 } } { 4 \pi } \cdot \frac { M } { d ^ { 3 } } =5×10−7×10(0.1)3= \sqrt { 5 } \times 10 ^ { - 7 } \times \frac { 10 } { ( 0.1 ) ^ { 3 } }= 5×10−3\sqrt { 5 } \times 10 ^ { - 3 }Tesla.