Question 287: Magnetism and Matter

Question

The ratio of magnetic field at the centre of a current carrying coil of radius $$r$$ to the magnetic field at distance $$r$$ from the centre of coil on its axis is $$\sqrt{x}: 1$$. The value of $$x$$ is __________

Accepted Answer

The magnetic field at the center of a loop (B
1
) is given by
$ B_1 = \frac{\mu_0 I}{2r} $
The magnetic field on the axis of the loop at a distance ( r ) from the center (B
2
) is given by
$ B_2 = \frac{\mu_0 Ir^2}{2(r^2 + d^2)^{3/2}} $
where ( d ) is the distance from the center of the coil along the axis. Since ( d = r ), we get
$ B_2 = \frac{\mu_0 I}{4\sqrt{2}r} $
The ratio of $ B_1 $ to $ B_2 $ is
$ \frac{B_1}{B_2} = \frac{\mu_0 I}{2r} 	imes \frac{4\sqrt{2}r}{\mu_0 I} = \sqrt{8} : 1 $
So, the value of ( x ) is 8.

Magnetism and Matter

The ratio of magnetic field at the centre of a current carrying coil of radius $r to the magnetic field at distance r from the centre of coil on its axis is \sqrt{x}: 1. The value of x$ is __________

Choose the correct answer: