Question

An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current I ampere and the radius of the circular loop is r metre. Then the magnetic induction B at the centre of the circular part is:

• A. zero
• B. $infty$
• C. $\frac{{\mu }_0}{4\pi }\frac{2I}{r}(\pi +1)$
• D. $\frac{{\mu }_0}{4\pi }\times \frac{2I}{R}(\pi -1)$

Answer 1

The correct option is D $\frac{{\mu }_0}{4\pi }\times \frac{2I}{R}(\pi -1)$

$\begin{array}{c}B=\left|\frac{\mu OI}{2\pi R}-\frac{\mu OI}{2R}\right|\\ B=\frac{\mu oi}{2R}\left(1-\frac{1}{11}\right)\\ =\frac{\mu oi}{2\pi R}\left(\pi -1\right)\\ =\frac{\mu o}{4\pi }\times \frac{2I}{R}\left(\pi -1\right)\end{array}$

$\therefore$ Option $D$ is correct answer.