The magnetic field at the center of current carrying circular loop is B 1. The magnetic field at a distance of √3 times radius of the given circular loop from the center on its axis is B2. The value of B1 / B2 will be

Question

The magnetic field at the center of current carrying circular loop is B 1. The magnetic field at a distance of √3 times radius of the given circular loop from the center on its axis is B2. The value of B1 / B2 will be (A) 9: 4 (B) 12: √5 (C) 8: 1 (D) 5: √3

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/8863bfaa691a316f5808836a66999f35-.png" /> B 1=(μ0 I /2 R ) B 2=(μ0 IR 2/2( R 2+3 R 2)3 / 2)=(1/8)((μ0 I /2 R ))=( B 1/8) ( B 1/ B 2)=(8/1)

Q. The magnetic field at the center of current carrying circular loop is $B_{1}$ . The magnetic field at a distance of $3$ times radius of the given circular loop from the center on its axis is $B_{2}$ . The value of $B_{1} / B_{2}$ will be

$9 : 4$

$12 : 5$

$8 : 1$

$5 : 3$

$B_{1} = \frac{μ _{0} I}{2 R}$
$B_{2} = \frac{μ _{0} I R ^{2}}{2 ( R ^{2} + 3 R ^{2} ) ^{3/2}} = \frac{1}{8} (\frac{μ _{0} I}{2 R}) = \frac{B _{1}}{8}$
$\frac{B _{1}}{B _{2}} = \frac{8}{1}$

Q. The magnetic field at the center of current carrying circular loop is B1​. The magnetic field at a distance of 3​ times radius of the given circular loop from the center on its axis is B2​. The value of B1​/B2​ will be

9:4

12:5​

8:1

5:3​