Question

Two flat circular coils are made of two identical wires each of length 20 cm, one coil has 4 turns while the second has 2. If the same current flows through the two, then find ratio of the field at their centre.

Answer 1

Length of wire$=20cm=0.2m$

radius of coil -1 $=\frac{0.2}{4\times 2\pi }=r_1$

radius of coil-2 $=\frac{0.2}{2\left(2\pi \right)}=r_2$

Using,

$\overrightarrow{B}=\frac{{\mu }_0}{2r}nI$

$=\frac{B_1}{B_2}=\frac{{\mu }_{0}4I}{2r_1}\times \frac{2r_2}{{\mu }_{0}2I}=\frac{2r_2}{r_1}$

$=\frac{2^2\left(4\pi \right)}{0.2}\times \frac{0.2}{4\pi }$

$\frac{B_2}{B_1}=\frac{1}{4}$