If B is the magnetic field at the centre of a circular loop of area A and its magnetic dipole moment is found to be n B A m μ 0 π , then what is the value of n + m ?

Step-by-step solution

Let r be the radius of the circular loop. ∴    A = π r 2 ⇒ r = A π Magnetic field at the centre of the loop is B = μ 0 I 2 r ⇒ B = μ 0 I 2 A π ⇒ I = 2 B μ 0 A π Now, magnetic moment of the loop is M = IA = 2 B μ 0 A π · A = 2 B μ 0 A 3 2 π ⇒ n = 2 and m = 1 . 5 ∴   n + m = 3 . 5