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
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 2 : 1
By the Biot-Savart law, the field at the centre of a circular coil of \( N \) turns and radius \( R \) is
\( \displaystyle B = \frac{\mu_0 N I}{2R} \)
With \( N \) and \( I \) the same for both coils, \( B \propto 1/R \).
\( R_1 = 10/2 = 5\,\mathrm{cm} \)
\( R_2 = 20/2 = 10\,\mathrm{cm} \)
\( \displaystyle \frac{B_1}{B_2} = \frac{R_2}{R_1} = \frac{10}{5} = \frac{2}{1} \)
The smaller coil gives the larger field, so the ratio is 2 : 1.