Question

A circular loop of radius $r$ is carrying current $I A$. The ratio of magnetic field at the center of circular loop and at a distance $r$ from the center of the loop on its axis is:

• A. $1: 3 \sqrt{2}$
• B. $2 \sqrt{2}: 1$
• C. $3 \sqrt{2}: 2$
• D. $1: \sqrt{2}$

Answer 1

Answer: (B)

Magnetic field due to current carrying circular loop on its axis is given as
$\frac{\mu_0 ir ^2}{2\left( r ^2+ x ^2\right)^{3 / 2}}$
At centre, $x=0, B_1=\frac{\mu_0 i}{2 r}$
At $x=r, B_2=\frac{\mu_0 i }{2 \times 2 \sqrt{2} r }$
$\frac{ B _1}{ B _2}=2 \sqrt{2}$