Two circular coils of diameter 10 cm and 20 cm, carrying equal currents have the same number of turns. The ratio of magnetic fields produced at the center of coils, respectively will be

2 : 1

The correct answer is Option (4) → 2 : 1

Magnetic field at the center of a circular coil: $B = \frac{\mu_0 N I}{2 R}$

Given: Diameters $D_1 = 10 \ \text{cm}$, $D_2 = 20 \ \text{cm} \text{ implies }R_1 = 5 \ \text{cm}, R_2 = 10 \ \text{cm}$

Currents and number of turns are equal: $I_1 = I_2$, $N_1 = N_2$

Magnetic field ratio: $\frac{B_1}{B_2} = \frac{\frac{\mu_0 N I}{2 R_1}}{\frac{\mu_0 N I}{2 R_2}} = \frac{R_2}{R_1} = \frac{10}{5} = 2$

Ratio of magnetic fields $B_1 : B_2 = 2 : 1$