Question

The magnetic field at the centre of a circular coil of radius r carrying current I is $B_1$. The field at the centre of another coil of radius 2r carrying the same current I is $B_2$. The ratio $\frac{B_1}{B_2}$ is

• A. $\frac{1}{2}$
• B. 1
• C. 2
• D. 4

Answer 1

The correct option is C 2

The magnetic field at the centre of a circular coil of radius R carrying current I can be calculated as:
$B=\frac{{\mu }_{o}l}{2R}$
$\therefore B_1=\frac{{\mu }_{o}l}{2r}$
$B_2=\frac{{\mu }_{o}l}{2\times \left(2r\right)}=\frac{{\mu }_{o}l}{4r}$
$\Rightarrow \frac{B_1}{B_2}=\frac{4r}{2r}=\frac{2}{1}=2$
Hence, the correct answer is option (3).