Question

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

• A. 2x
• B. 4x
• C. $\frac{x}{4}$
• D. $\frac{x}{8}$

Answer 1

Answer: (D)

Magnetic field at the center of the current carrying loop is given by
$B=$ $\left({\mu }_0/4\pi \right)\times (2\pi i/a)=\left({\mu }_{0}i\right)/2a.$
Magnetic moment at the center of the current carrying loop is given by
$M=\pi a^2$
thus $B/M={\mu }_0/\left(2\pi a^3\right)=x($ given $)$
when both current and radius are doubled ratio become $x/8$ times.