JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Magnetic Effects of Current

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Magnetic fields at two points on the axis of a circular coil at a distance of 0.05 m and 0.2 m from the centre are in the ratio

8 : 1

. The radius of coil is

(A)0.15 m
(B)1.0 m
(C)0.1 m✓ Correct
(D)0.2 m

Answer: (C)

Solution

The magnetic field on the axis of a circular coil at distance

x

from the center is:

B = \frac{μ _{0} N i r ^{2}}{2 ( r ^{2} + x ^{2} ) ^{3/2}}

Given

B_{0.05} / B_{0.2} = 8/1

\frac{( r ^{2} + 0. 2 ^{2} ) ^{3/2}}{( r ^{2} + 0.0 5 ^{2} ) ^{3/2}} = 8

\frac{r ^{2} + 0.04}{r ^{2} + 0.0025} = 8^{2/3} = 4

r^{2} + 0.04 = 4 r^{2} + 0.01

3 r^{2} = 0.03

r^{2} = 0.01 \Rightarrow r = 0.1 m

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Single correct option

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