Question

A circular coil of radius $2R$ is carrying current $i$.The ratio of magnetic fields at the centre of the coil and at a point at a distance $6R$ from the centre of the coil on the axis of the coil is :

• A. $10$
• B. $10\sqrt{10}$
• C. $20\sqrt{10}$
• D. $20\sqrt{5}$

Answer 1

The correct option is B $10\sqrt{10}$

At the centre of the coil, $B_1=\frac{{\mu }_{0}i}{2\times 2R}=\frac{{\mu }_{0}i}{4R}$

On the axis of the coil, $B_2=\frac{{\mu }_{0}i(2R{)}^2}{2(4R^2+x^2{)}^{3/2}}$

Put X = 6R

$\Rightarrow B_2=\frac{{\mu }_{0}i}{2R}\times \frac{4}{{40}^{3/2}}=\frac{{\mu }_{0}i}{40\sqrt{10}R}$

$\frac{B_1}{B_2}=10\sqrt{10}$