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
$B=\frac{{\mu }_0}{4\pi }\left(\frac{2\pi i}{a}\right)=\frac{{\mu }_{0}i}{2a}$
The magnetic moment at the centre of current carrying loop is
given by $M=i(\pi a^2)$
Thus, $\frac{B}{M}=\frac{{\mu }_{0}i}{2a}\times \frac{1}{i\pi a^2}=\frac{{\mu }_0}{2\pi a^3}=x(given)$
When both the current and the radiuf are doubled, the ratio
becomes
$\frac{{\mu }_0}{2\pi (2a{)}^3}=\frac{{\mu }_0}{8(2\pi a^3)}=\frac{x}{8}$