The ratio of magnetic field at the centre of a current carrying circular coil to its magnetic moment is x , if the current and the radius both are doubled. The new ratio will become

Step-by-step solution

Magnetic field at the centre of current carrying circular coil B= ₀ I 2 r where, I= current and r= radius. Magnetic dipole moment, aligned & m=I A=I r² Given, & B m =x & ₀ I 2 r & ₀ I r² =x ...(i) aligned When current and radius, both are doubled, then aligned B^ m^ &= ₀ 2 I 2 2 r (2 I)(2 r)² &= ₀ I 2 r 8 r² I = ₀ 16 r³ &= 1 8 ₀ 2 r³ = x 8 [from Eq. (i)] aligned