question_answer

Two identical short bar magnets, each having magnetic moment of \[10\text{ }A{{m}^{2}},\] 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 \[0.2\text{ }m,\] the resultant magnetic induction at a point midway between them is \[({{\mu }_{0}}=4\pi \times {{10}^{-7}}H{{m}^{-1}})\]

A) \[\sqrt{2}\times {{10}^{-7}}\,tesla\]

B) \[\sqrt{5}\times {{10}^{-7}}\,tesla\]

C) \[\sqrt{2}\times {{10}^{-3}}\,tesla\]

D) \[\sqrt{5}\times {{10}^{-3}}\,tesla\]

Correct Answer: D

Solution :

From figure \[{{B}_{net}}=\sqrt{B_{a}^{2}+B_{e}^{2}}\] \[=\sqrt{{{\left( \frac{{{\mu }_{0}}}{4\pi }.\frac{2M}{{{d}^{3}}} \right)}^{2}}+{{\left( \frac{{{\mu }_{0}}}{4\pi }.\frac{M}{{{d}^{3}}} \right)}^{2}}}\] \[=\sqrt{5}.\frac{{{\mu }_{0}}}{4\pi }.\frac{M}{{{d}^{3}}}=\sqrt{5}\times {{10}^{-7}}\times \frac{10}{{{(0.1)}^{3}}}=\sqrt{5}\times {{10}^{-3}}tesla\]