Question

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

• A. \(\frac{7}{2}\hat k\; Am^2\)
• B. \(-\frac{7}{2}\hat k\;Am^2\)
• C. \(7\hat k\;Am^2\)
• D. \(-7\hat k\;Am^2\)

Answer 1

The Correct Option is B

The net magnetic moment of this system of two circular loops is : 

\(μ_1 = πr^2_1 \times I_1\)

\(μ_2 = πr^2_2 \times I_2\)

Hence,\(μ_{net} = (μ_2-μ_1)(-\hat k)\)

= \(π(r^2_2-r^2_1)I(-\hat k)\)

= \(3.142 \times (0.5^2-03^2)\times 7(-\hat k)\)

= \(- \frac{7}{2}\hat  k \;Am^2\)