JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Magnetic Effects of Current

Two concentric circular loops of radii

r_{1} = 30

cm and

r_{2} = 50

cm are placed in X-Y plane as shown in the figure. A current

I = 7

A is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately :

Answer: (B)

Solution

The magnetic moment of a current loop is

M = I A \overset{n}{^}

, where

\overset{n}{^}

is determined by the right-hand rule. For the outer loop (r=0.5 m, clockwise from above),

M_{1} = - I π (0.5)^{2} \hat{k}

. For the inner loop (r=0.3 m, counterclockwise from above),

M_{2} = + I π (0.3)^{2} \hat{k}

. The net moment is

M = - 7 π (0.25 - 0.09) \hat{k} = - 7 π (0.16) \hat{k} \approx - 3.52 \hat{k}

^{2}

\approx - \frac{7}{2} \hat{k}

^{2}

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Single correct option