Question

A portion of a conductive wire is bent in the form of a semicircle of radius r as shown below in figure. At the centre of semicircle, the magnetic induction will be:

• A. zero
• B. inifinite
• C. $\frac{{\mu }_0}{4\pi }\cdot \frac{\pi i}{2r}tesla$
• D. $\frac{{\mu }_0}{4\pi }\cdot \frac{\pi i}{r}tesla$

Answer 1

The correct option is D $\frac{{\mu }_0}{4\pi }\cdot \frac{\pi i}{r}tesla$

The straight part will not contribute magnetic field at the centre of the semicircle because every element of the straight part will be 0${}^o$ or 180${}^o$ with the line joining the centre and the element.

Due to circular portion, the field is $\frac{1}{2}\frac{{\mu }_{0}i}{2r}=\frac{{\mu }_{0}i}{4r}$

Hence, total field at O $=\frac{{\mu }_{0}i}{4r}tesla$