Question

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

• A.
• B.
• C. Zero
• D. Infinite

Answer 1

The correct option is B

The given shape is equivalent to the following diagram
The field at o due to straight part of conductor is $B_1=\frac{{\mu }_0}{4\pi }.\frac{2i}{r}\odot$.

The field at o due to circular coil is $B_2=\frac{{\mu }_0}{4\pi }.\frac{2\pi i}{r}\otimes$. Both fields will act in the opposite direction, hence the total field at O.
i.e. $B=B_2-B_1=\left(\frac{{\mu }_0}{4\pi }\right)\times (\pi -1)\frac{2i}{r}=\frac{{\mu }_0}{4\pi }.\frac{2i}{r}(\pi -1)$