Question

Two points P and Q are on the axis at distances r and 3r from the centre of a circular coil of radius r and carrying a current. The ratio of magnetic inductions at P and Q is :

• A. 3 : 1
• B. $1:5\sqrt{5}$
• C. $5\sqrt{5}:1$
• D. 1 : 3

Answer 1

The correct option is C $5\sqrt{5}:1$

$\left|B\right|$ at P =$\frac{2{\mu }_{0}i\pi r^2}{4\pi \sqrt[3]{3r^2+r^2}}$

= $\frac{2{\mu }_{0}i\pi r^2}{4\pi \sqrt[3]{32r^2}}$

$\left|B\right|$ at Q =$\frac{2{\mu }_0.i.\pi r^2}{4\pi \sqrt[3]{3r^2+9r^2}}$

= $\frac{2{\mu }_0.i.\pi r^2}{4\pi \sqrt[3]{32r^2}\times \sqrt[3]{35}}$

Ratio =$5\sqrt{5}:1$