question_answer

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 \[({{\mu }_{0}}=4\pi \times {{10}^{-7}}H{{m}^{-1}})\]                      [EAMCET 2005]

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.