Question

A circular coil carrying a certain current produces a magnetic field $B_1$ at its center. The coil is now rewound so as to have 3 turns and the same current is passed through it. The new magnetic field at the centre is

• A. $B_1/2$
• B. $9B_1$
• C. $B_1/3$
• D. $3B_1$

Answer 1

Answer: (D)

(d) $3B_1$

Answer 2

The magnetic field at the center of a circular coil is given by $B = \frac{\mu_0 n I}{2R}$, where $n$ is the number of turns, $I$ is the current, and $R$ is the radius. Let the original coil have $n_1$ turns and radius $R$. The magnetic field at its center is $B_1 = \frac{\mu_0 n_1 I}{2R}$. The coil is rewound to have 3 turns, so the new number of turns is $n_2 = 3n_1$ (assuming the radius $R$ remains the same and the same current $I$ is passed). The new magnetic field at the center is $B_2 = \frac{\mu_0 n_2 I}{2R} = \frac{\mu_0 (3n_1) I}{2R}$. Comparing $B_2$ with $B_1$: $B_2 = 3 \left(\frac{\mu_0 n_1 I}{2R}\right) = 3B_1$.