The magnitude of the magnetic field at the center of a current carrying circular coil is directly proportional to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Permeability of free space and current and inversely proportional to radius of the coil
By the Biot-Savart law, every element of a circular coil is at the same distance \( r \) from the centre and perpendicular to the radius, so the contributions add up to
\( \displaystyle B = \frac{\mu_0 I}{2r} \)
So \( B \) is directly proportional to \( \mu_0 \) and \( I \), and inversely proportional to \( r \).
NCERT (2026-27):
Magnetic Field on the Axis of a Circular Current Loop – “… As a special case of the above result, we may obtain the field at the centre of the loop. Here x = 0, and we obtain,
\( \displaystyle \mathbf{B}_0 = \frac{\mu_0 I}{2R}\,\hat{\mathbf{i}} \qquad (4.12) \)”