Two concentric circular coils of 10 turns each are situated in the same plane. Their radii are 20 cm and 40 cm and they carry 0.2 A and 0.3 A currents respectively in opposite directions. The magnetic field at the center is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \displaystyle\frac{5}{4}\mu_0\,\mathrm{T} \)
At the centre of a circular coil of N turns the field is \( B = \mu_0NI/(2r) \). Both coils share the same centre and carry currents in opposite directions, so their fields at the centre are opposite and the net field is the difference.
\( \displaystyle B_1 = \frac{\mu_0\times10\times0.2}{2\times0.20} = 5\,\mu_0 \)
\( \displaystyle B_2 = \frac{\mu_0\times10\times0.3}{2\times0.40} = \frac{15}{4}\,\mu_0 \)
\( \displaystyle B = B_1 - B_2 = \left(5-\frac{15}{4}\right)\mu_0 = \frac{5}{4}\,\mu_0\ \mathrm{T} \)