Question

Two concentric circular loops of radii $0.08 \, m$ and $0.1 \, m$ carry currents such that magnetic field at the centre is zero. If the current in the outer loop is $8 \, A$ clockwise, current in the inner loop is

• A. 6.4 A anti-clockwise
• B. 6.4 A clockwise
• C. 8 A anti-clockwise
• D. 3.2 A clockwise

Answer 1

Answer: (A)

6.4 A anti-clockwise

Answer 2

Here, $R_1 = 0.1 \, m, R_2 = 0.08 \, m, I_1 = 8 \, A$ Magnetic field at centre $O$ due to current in outer loop, $\vec{B}_1 = \frac{\mu_0 I_1}{2R_1} \otimes$ Let the current in inner loop be $I_2$ and magnetic field at centre $O$ due to it be $\vec{B}_2$ As $\vec{ B}_1 + \vec{ B}_2$ or $\vec{ B}_1 = - \vec{ B}_2$ $\therefore \, \, I_2$ must be anti-clockwise and $|\vec{B}_1 | = | \vec{B}_2|$ or, $\frac{\mu_0 I_1}{2 R_1} = \frac{\,u_0 I_2}{2 R_2}$ $\Rightarrow \, \, I_2 = \frac{I_1 }{R_1} \times R_2 = \frac{8}{0.1} \times 0.08$ $= 6.4 \, A$