question_answer

A wire in the form of a square of side ?a? carries a current i. Then the magnetic induction at the centre of the square wire is (Magnetic permeability of free space =\[{{\mu }_{o}})\] [EAMCET 2001]

A)            \[\frac{{{\mu }_{0}}i}{2\pi a}\]                                         

B)            \[\frac{{{\mu }_{0}}i\sqrt{2}}{\pi a}\]

C)            \[\frac{2\sqrt{2}{{\mu }_{o}}i}{\pi a}\]                         

D)            \[\frac{{{\mu }_{0}}i}{\sqrt{2}\pi \,a}\]

Correct Answer: C

Solution :

                   \[{{B}_{0}}=4\times \frac{{{\mu }_{0}}}{4\pi }\times \frac{i}{\left( a/2 \right)}(\sin 45{}^\circ +\sin 45{}^\circ )\]                    \[=4\times \frac{{{\mu }_{0}}}{4\pi }\times \frac{2i}{a}\times \frac{2}{\sqrt{2}}\]            \[=\frac{{{\mu }_{0}}i2\sqrt{2}}{\pi a}\]