Question

An infinite straight current carrying conductor is bent in such a way that a circular loop is formed on it as shown in the figure. If the radius of the loop is R, the magnetic field at the centre of the loop is :

• A. $\frac{{\mu }_0}{4\pi }\cdot \frac{2I}{R}\pi$
• B. Infinite
• C. $\frac{{\mu }_0}{4\pi }\cdot \frac{2I}{R}(\pi +1)$
• D. Zero

Answer 1

The correct option is C $\frac{{\mu }_0}{4\pi }\cdot \frac{2I}{R}(\pi +1)$

The field at point O will be the resultant of the fields due so circular loop and straight wire. So, the field due to both the loop and the wire at centre O will be out of the page.
The magnetic field at the centre (O) of the loop.
$B=\frac{{\mu }_0}{4\pi }\frac{2I}{R}+\frac{{\mu }_{0}2\pi I}{4\pi R}$
$\Rightarrow B=\frac{{\mu }_0}{4\pi }\frac{2I}{R}[1+\pi ]$