Question

An infinite long straight wire is bent into a semicircle of radius $R$, as shown in the figure. A current $I$ is sent through the conductor. The magnetic field at the centre of the semicircle is :

• A. $\infty$
• B. $0$
• C. $\frac{{\mu }_0}{4R}I$
• D. $\frac{{\mu }_{0}I}{4\pi R}(\pi +1)$

Answer 1

The correct option is C $\frac{{\mu }_0}{4R}I$

Magnetic field due to straight portion of the wire $=0$

Magnetic field due to circular portion of the wire:

$=\frac{1}{2}\left(\frac{{\mu }_{0}I}{2R}\right)=\frac{{\mu }_{0}I}{4R}$

Hence the correct answer is $\frac{{\mu }_{0}I}{4R}$