Question

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces magnetic field $B_1$, at its centre when a current $I$ passes through it. The second wire is bent into a coil with three identical loops adjacent to each other produces magnetic field $B_2$ at the centre of the loops when current $\frac{I}{3}$ passes through it. The ratio $B_1:B_2$ is :

• A. $1:1$
• B. $1:3$
• C. $1:9$
• D. $9:1$

Answer 1

The correct option is B $1:3$

Magnetic field due to the first loop , $B_1=\frac{{\mu }_{0}I}{2r}$
For 2nd wire, there are three loops (n=3) so total current enclosed by the loops ,

$I_{en}=I/3+I/3+I/3=I$

Radius of second loop$=r/3$ because the original wires are identical.
magnetic field $B_2=\frac{{\mu }_0{I}_{en}}{2r/3}=\frac{{\mu }_{0}3I}{2r}$
$\frac{B_1}{B_2}=\frac{1}{3}$