question_answer

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

A) \[\frac{{{\mu }_{0}}}{4\pi }\sqrt{2}\,\frac{M}{{{d}^{3}}}\]                 

B) \[\frac{{{\mu }_{0}}}{4\pi }(\sqrt{3})\,\frac{M}{{{d}^{3}}}\]

C) \[\left( \frac{2{{\mu }_{0}}}{4\pi } \right)\,\frac{M}{{{d}^{3}}}\]                      

D) \[\frac{{{\mu }_{0}}}{4\pi }(\sqrt{5})\,\frac{M}{{{d}^{3}}}\]

Correct Answer: D

Solution :

\[=\,\,\,\,\sqrt{{{\left( \frac{2kM}{{{d}^{3}}} \right)}^{2}}+{{\left( \frac{kM}{{{d}^{3}}} \right)}^{2}}}=\frac{kM}{{{d}^{3}}}\,(\sqrt{5})\]