First slide

Magnetic field due to a current carrying circular ring

Question

The ratio of the magnetic field at the centre of a current carrying coil of the radius a to that at a distance a from centre of the coil and on the axis of the coil is

Moderate

A

$\frac{1}{\sqrt{2}}$
B

$\sqrt{2}$
C

$\frac{1}{2 \sqrt{2}}$
D

$2 \sqrt{2}$

Solution

$\frac{B_{c}}{B_{a}} = {(1 + \frac{x^{2}}{r^{2}})}^{3 / 2} = {(1 + \frac{a^{2}}{a^{2}})}^{3 / 2} = {(1 + 1)}^{3 / 2} = 2 \sqrt{2}$

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