Question

An infinitely long conductor is bent into a circle as shown in figure. It carries a current $i$ ampere and the radius of loop is $R$ metre. The magnetic induction at the centre of loop is :

• A. $ \frac{\mu _{0}}{4\pi }\frac{2I}{R}(\pi +1)$ tesla
• B. $ \frac{\mu_{0}}{4\pi }\frac{2I}{R}(\pi -1)$ tesla
• C. $ \frac{\mu _{0}}{4\pi }\frac{I}{2R}(\pi +1)$ tesla
• D. zero

Answer 1

Answer: (A)

The given shape is equivalent to the following diagram
The field at o due to straight part of conductor is
$B_{1}=\frac{\mu_{0}}{4 \pi^{*}} \frac{2 i}{r} \odot$.

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. $B=B_{2}-B_{1}$
$=\left(\frac{\mu_{0}}{4 \pi}\right) \times(\pi-1) \frac{2 i}{r}$
$=\frac{\mu_{0}}{4 \pi} \cdot \frac{2 i}{r}(\pi-1)$