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:

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 √2 (B) 2 √2: 1 (C) 3 √2: 2 (D) 1: √2

Tardigrade Admin · Accepted Answer

Magnetic field due to current carrying circular loop on its axis is given as (μ0 ir 2/2( r 2+ x 2)3 / 2) At centre, x=0, B1=(μ0 i/2 r) At x=r, B2=(μ0 i /2 × 2 √2 r ) ( B 1/ B 2)=2 √2

Q. 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:

$1 : 32$

$22 : 1$

$32 : 2$

$1 : 2$

Magnetic field due to current carrying circular loop on its axis is given as
$\frac{μ _{0} i r ^{2}}{2 ( r ^{2} + x ^{2} ) ^{3/2}}$
At centre, $x = 0, B_{1} = \frac{μ _{0} i}{2 r}$
At $x = r, B_{2} = \frac{μ _{0} i}{2 \times 2 2 r}$
$\frac{B _{1}}{B _{2}} = 22$

Q. A circular loop of radius r is carrying current IA. 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:

1:32​

22​:1

32​:2

1:2​