Magnetic Effects Of Current Question 2

Question 2 - 24 January - Shift 1

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

(1) $1: 3 \sqrt{2}$

(2) $3 \sqrt{2}: 2$

(3) $2 \sqrt{2}: 1$

(4) $1: \sqrt{2}$

Show Answer

Answer: (3)

Solution:

Formula: Magnetic field due to circular loop

Magnetic field due to current carrying circular loop on its axis is given as

$\frac{\mu_0 ir^{2}}{2(r^{2}+x^{2})^{3 / 2}}$

At centre, $x=0, B_1=\frac{\mu_0 i}{2 r}$

At $x=r, B_2=\frac{\mu_0 i}{2 \times 2 \sqrt{2} r}$

$\frac{B_1}{B_2}=2 \sqrt{2}$