A and B are the two concentric circular conductors of center O and carrying currents I1 and I2 as shown in the adjacent figure. If ratio of their radii is 1: 2 and ratio of the flux densities at O due to A and B is 1: 3 then the value of I1 / I2 is

Question

A and B are the two concentric circular conductors of center O and carrying currents I1 and I2 as shown in the adjacent figure. If ratio of their radii is 1: 2 and ratio of the flux densities at O due to A and B is 1: 3 then the value of I1 / I2 is <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/578ec6e653035067ad199f4d7aa5e1ae-.png" /> (A) 1 / 6 (B) 1 / 4 (C) 1 / 3 (D) 1 / 2

Tardigrade Admin · Accepted Answer

r1: r2=1: 2 and B1: B2=1: 3 (flux density) B =(μ o /4 π) (2 π nI / R ) (I1/I2)=(B1/B2) (R1/R2)=(1 × 1/3 × 2)=(1/6) (I1/I2)=(1/6)

Q. $A$ and $B$ are the two concentric circular conductors of center $O$ and carrying currents $I_{1}$ and $I_{2}$ as shown in the adjacent figure. If ratio of their radii is 1: 2 and ratio of the flux densities at $O$ due to $A$ and $B$ is 1 : 3 then the value of $I_{1} / I_{2}$ is

$1/6$

$1/4$

$1/3$

$1/2$

$r_{1} : r_{2} = 1 : 2$ and $B_{1} : B_{2} = 1 : 3$ (flux density)
$B = \frac{μ _{o}}{4 π} \frac{2 πn I}{R}$
$\frac{I _{1}}{I _{2}} = \frac{B _{1}}{B _{2}} \frac{R _{1}}{R _{2}} = \frac{1 \times 1}{3 \times 2} = \frac{1}{6}$
$\frac{I _{1}}{I _{2}} = \frac{1}{6}$

Q. A and B are the two concentric circular conductors of center O and carrying currents I1​ and I2​ as shown in the adjacent figure. If ratio of their radii is 1: 2 and ratio of the flux densities at O due to A and B is 1 : 3 then the value of I1​/I2​ is

1/6

1/4

1/3

1/2