Question

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

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

Answer 1

Answer: (D)

$20 \sqrt{10}$

Answer 2

At the centre of coil ,$B_{1} = \frac{\mu_{0}}{4\pi} \frac{2\pi l}{2R}$
At a distance $6R$ from centre of coil and on the axis of coil, $B_{2} = \frac{\mu_{0}}{4\pi} \frac{2\pi I\left(2R\right)^{2}}{\left[\left(2R\right)^{2}+\left(6R\right)^{2}\right]^{3/2}}$
$B_{2} = \frac{\mu_{0}}{4\pi} \frac{2\pi I \times 4R^{2}}{\left(2\sqrt{10}\right)^{3}R^{3}}$
$\therefore \:\:\frac{B_{1}}{B_{2}} = 10 \sqrt{10}$