question_answer

A part of a long wire carrying a current i is bent into a circle of radius r as shown in figure. The net magnetic field at the centre O of the circular loop is                              [UPSEAT 2002]

A)            \[\frac{{{\mu }_{o}}i}{4r}\]

B)            \[\frac{{{\mu }_{o}}i}{2r}\]

C)            \[\frac{{{\mu }_{o}}i}{2\pi r}(\pi +1)\]

D)            \[\frac{{{\mu }_{o}}i}{2\pi r}(\pi -1)\]

Correct Answer: C

Solution :

                   The given circuit can be considered as follows                    \[{{B}_{\text{loop}}}=\frac{{{\mu }_{0}}i}{2r}\]¤                              \[{{B}_{\text{conductor}}}=\frac{{{\mu }_{0}}i}{2\pi r}\]¤        \[{{B}_{\text{net}}}=\frac{{{\mu }_{0}}i}{2\pi r}(\pi +1)\]¤