The magnetic field at the center of current carrying circular loop is $\mathrm{B}_{1}$. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is $\mathrm{B}_{2}$. The value of $\mathrm{B}_{1} / \mathrm{B}_{2}$ will be

JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Magnetic Effects of Current

The magnetic field at the center of current carrying circular loop is

B_{1}

. The magnetic field at a distance of

3

times radius of the given circular loop from the center on its axis is

B_{2}

. The value of

B_{1} / B_{2}

will be

Answer: (C)

The magnetic field at the center of a circular loop is

B_{1} = \frac{μ _{0} I}{2 R}

.

The magnetic field on the axis at distance

x = 3 R

from the center is given by

B_{2} = \frac{μ _{0} IR ^{2}}{2 ( R ^{2} + x ^{2} ) ^{3/2}}

.

Substituting

x = 3 R

B_{2} = \frac{μ _{0} IR ^{2}}{2 ( R ^{2} + 3 R ^{2} ) ^{3/2}} = \frac{μ _{0} IR ^{2}}{2 ( 4 R ^{2} ) ^{3/2}} = \frac{μ _{0} I}{2 \cdot 8 R} = \frac{B _{1}}{8}

.

Therefore,

\frac{B _{1}}{B _{2}} = 8 : 1

JEE Main · 2022 · 28 Jul 2022 · Shift 2 · Single correct option