A steady current flow in a long wire. It is bent into a circular loop of one turn and the magnetic field at the centre of the coil is B . If the same wire is bent into a circular loop of n turns, the magnetic field at the centre of the coil is

Step-by-step solution

The magnetic field a circular coil (for n number of loops) B = μ 0 n i 2 r When, n 1 = 1 , n 2 = 2 2 π r 1 = n × 2 π r 2 ⇒ r 1 r 2 = n 1 So B 1 B 2 = μ 0 n 1 i 2 r 1 μ 0 n 2 i 2 r 2 B B 2 = n 1 n 2 . r 1 r 2 B B 2 = 1 n . 1 n ⇒ B 2 = n 2 B