Question

A conducting circular loop of radius $a$ is connected to two long, straight wires. The straight wires carry a current $i$ as shown in figure. Find the magnetic field $B$ at the centre of the loop.

• A. $Zero$
• B. $\frac{{\mu }_{0}I}{2a}$
• C. $\frac{{\mu }_{0}I}{a}$
• D. $\frac{{\mu }_{0}I}{a}+\frac{{\mu }_{0}I}{2\pi a}$

Answer 1

The correct option is A $Zero$

From figure,

The magnetic field at the center due to $ABC$ is,

$B_1=\frac{{\mu }_{0}I}{4r}$. . . . . . . .(1)

Inward direction

The magnetic field at the center due to $ADC$ is,

$B_2=\frac{{\mu }_{0}I}{4r}$. . . . . . .(2)

Outward direction.

The net magnetic field at the center due to circle is zero.

$B=B_1-B_2=0$

The correct option is A.