The magnetic field at the centre of a circular current carrying loop of radius R is B1. The magnetic field on its axis at a distance R from the centre is B2. The value of B1: B2 will be

Question

The magnetic field at the centre of a circular current carrying loop of radius R is B1. The magnetic field on its axis at a distance R from the centre is B2. The value of B1: B2 will be (A) √2: 1 (B) 1: √2 (C) 2 √2: 1 (D) 1: 2 √2

Tardigrade Admin · Accepted Answer

B1=(μ0 i/2 R) B2=(μ0 i R2/2(R2+x2)3 / 2) =(μ0 I/2 × 2 √2 R) (B1/B2)=(2 √2/1)

Q. 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

$2 : 1$

$1 : 2$

$22 : 1$

$1 : 22$

$B_{1} = \frac{μ _{0} i}{2 R}$
$B_{2} = \frac{μ _{0} i R ^{2}}{2 ( R ^{2} + x ^{2} ) ^{3/2}}$
$= \frac{μ _{0} I}{2 \times 2 2 R}$
$\frac{B _{1}}{B _{2}} = \frac{2 2}{1}$

Q. The magnetic field at the centre of a circular current carrying loop of radius R is B1​. The magnetic field on its axis at a distance R from the centre is B2​. The value of B1​:B2​ will be

2​:1

1:2​

22​:1

1:22​