JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Magnetic Effects of Current

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The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it, is B. The magnetic field at a point along the axis at a distance

\frac{r}{2}

from the centre is :

(A) $B /2$
(B)2 B
(C) $(\frac{2}{5})^{3} B$ ✓ Correct
(D) $(\frac{2}{3})^{3} B$

Answer: (C)

Solution

The magnetic field at the center of a circular coil is

B_{C} = \frac{μ _{0} I}{2 r}

.

The magnetic field on the axis at distance

x

from center is:

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

x = \frac{r}{2}

B_{a} = \frac{μ _{0} I r ^{2}}{2 ( \frac{r ^{2}}{4} + r ^{2} ) ^{3/2}} = \frac{μ _{0} I r ^{2}}{2 ( \frac{5 r ^{2}}{4} ) ^{3/2}}

= \frac{μ _{0} I r ^{2}}{2 r ^{3}} \cdot (\frac{4}{5})^{3/2} = \frac{μ _{0} I}{2 r} \cdot (\frac{2}{5})^{3} = B (\frac{2}{5})^{3}

The answer is (C).

JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Single correct option

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JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Magnetic Effects of Current

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