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)

$2 \sqrt{2}: 1$

Answer 2

The correct answer is (B) : $2\sqrt2:1$
Magnetic field due to current carrying circular loop on its axis is given as $\frac{μ_0​ir^2​}{2(r^2+x^2)^{3/2}}$

At centre, $x=0,B_1​=\frac{μ_0​i}{2r}​$

At x=r ,$B_2​=\frac{μ_0​i}{2×2\sqrt2​r}$​

$\therefore\frac{B_1}{​B_2}​​=2\sqrt2 :1.$