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
$B =$ $\left(\mu_{0} / 4 \pi\right) \times(2 \pi i / a )=\left(\mu_{0} i \right) / 2 a .$
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.