Question

A part of a long wire a 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

• A. $\frac{{\mu }_{0}i}{4r}$
• B. $\frac{{\mu }_{0}i}{2r}$
• C. $\frac{{\mu }_{0}i}{2\pi r}(\pi +1)$
• D. $\frac{{\mu }_{0}i}{2\pi r}(\pi -1)$

Answer 1

The correct option is B $\frac{{\mu }_{0}i}{2r}$

The given circuit can be considered as follows

$B_{loop}=\frac{{\mu }_{0}i}{2r}\odot$

$B_{conductor}=\frac{{\mu }_{0}i}{2\pi r}\odot$

So, the net magnetic field is:

$B_{net}=\frac{{\mu }_{0}i}{2\pi r}(\pi +1)\odot$