question_answer

On connecting a battery to the two comers of a diagonal of a square conductor frame of side \[a,\] the magnitude of the magnetic field at the centre will be

A)  zero                                     

B)  \[\frac{{{\mu }_{0}}}{\pi a}\]

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

D) \[\frac{4{{\mu }_{0}}i}{\pi a}\]

Correct Answer: A

Solution :

Resultant intensity at centre \[B={{B}_{1}}+{{B}_{2}}+{{B}_{3}}+{{B}_{4}}\] \[B=\frac{{{\mu }_{0}}}{4\pi }\frac{2I}{a/2}+\frac{{{\mu }_{0}}}{4\pi }\,\frac{2I}{a/2}-\frac{{{\mu }_{0}}}{4\pi }\frac{2I}{a/2}-\frac{{{\mu }_{0}}}{4\pi }\frac{2I}{a/2}\] \[B=0\]