JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Magnetic Effects of Current

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 :

(A) $1 : 32$
(B) $32 : 2$
(C) $22 : 1$ ✓ Correct
(D) $1 : 2$

Answer: (C)

Solution

At the centre of the loop the field is

B_{1} = \frac{μ _{0} I}{2 r}

. On the axis a distance

r

from the centre,

B_{2} = \frac{μ _{0} I r ^{2}}{2 ( r ^{2} + r ^{2} ) ^{3/2}} = \frac{μ _{0} I r ^{2}}{2 ( 2 r ^{2} ) ^{3/2}} = \frac{μ _{0} I}{4 2 r}

. Dividing the first by the second,

\frac{B _{1}}{B _{2}} = 22

, so the two fields are in the ratio

22 : 1

JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Single correct option

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