question_answer

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

A) \[\frac{{{\mu }_{0}}i}{4r}\]                  

B)   \[\frac{{{\mu }_{0}}i}{2r}\]

C) \[\frac{{{\mu }_{0}}i}{2\pi r}(\pi +1)\]              

D) \[\frac{{{\mu }_{0}}i}{2\pi r}(\pi -1)\]

Correct Answer: C

Solution :

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