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)

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, $B_2=\frac{{\mu }_0}{4\pi }\frac{2\pi I{\left(2R\right)}^2}{{\left[{\left(2R\right)}^2+{\left(6R\right)}^2\right]}^{3/2}}$
$B_2=\frac{{\mu }_0}{4\pi }\frac{2\pi I\times 4R^2}{{\left(2\sqrt{10}\right)}^3{R}^3}$
$\therefore \frac{B_1}{B_2}=10\sqrt{10}$