Question

The ratio of magnetic field and magnetic moment at the
centre of a current carrying circular loop is X. When
both the current and radius is doubled the ratio will be

• A. x/8
• B. x/4
• C. x/2
• D. 2x

Answer 1

Answer: (A)

The magnetic field at the centre of a current carrying loop is
given by
$ B=\frac {\mu _0}{4 \pi} \bigg (\frac {2 \pi i}{a}\bigg )=\frac {\mu _0i}{2a} $
The magnetic moment at the centre of current carrying loop is
given by $M=i(\pi a^2) $
Thus, $ \frac {B}{M}= \frac {\mu _0i}{2a} \times \frac {1}{i \pi a^2}= \frac {\mu _0}{2 \pi a^3}=x(given) $
When both the current and the radiuf are doubled, the ratio
becomes
$ \frac {\mu_0}{2 \pi (2a)^3}= \frac {\mu_0}{8(2 \pi a^3)}= \frac {x}{8} $