Question

Magnetic fields at two points on the axis of a circular coil at a distance of $0.05m$ and $0.2m$ from the centre are in the ratio $8:1.$ The radius of coil is____

• A. $0.2m$
• B. $0.1m$
• C. $0.15m$
• D. $1.0m$

Answer 1

Answer: (B)

We know, the magnetic field on the axis of a current carrying circular ring is given by
$B=\frac{{\mu }_0}{4\pi }\frac{2NIA}{{\left(R^2+x^2\right)}^{3/2}}$
$\therefore \frac{B_1}{B_2}=\frac{8}{1}={\left[\frac{R^2+(0.2{)}^2}{R^2+(0.05{)}^2}\right]}^{3/2}$
$4\left[R^2+(0.05{)}^2\right]=\left[R^2+(0.2{)}^2\right]$
$4R^2-R^2=(0.2{)}^2-4\times (0.05{)}^2$
$4R^2-R^2=(0.2{)}^2-(0.1{)}^2$
$3R^2=0.3\times 0.1$
$R^2=(0.1{)}^2\Rightarrow R=0.1$