Question

The magnetic field at the centre of a circular current carrying loop of radius $R$ is $B_{1}$. The magnetic field on its axis at a distance $R$ from the centre is $B_{2}$. The value of $B_{1}: B_{2}$ will be

• A. $\sqrt{2}: 1$
• B. $1: \sqrt{2}$
• C. $2 \sqrt{2}: 1$
• D. $1: 2 \sqrt{2}$

Answer 1

Answer: (C)

$B_{1}=\frac{\mu_{0} i}{2 R}$
$B_{2}=\frac{\mu_{0} i R^{2}}{2\left(R^{2}+x^{2}\right)^{3 / 2}}$
$=\frac{\mu_{0} I}{2 \times 2 \sqrt{2} R}$
$\frac{B_{1}}{B_{2}}=\frac{2 \sqrt{2}}{1}$