P and Q are two concentric circular loop carrying current i 1 and i 2 as shown in figure. If ratio of their radii is 3: 2 and ratio of the flux densities at the centre O due to P and Q is 1: 3 then the value of ( i 1/ i 2) will be :-

Question

P and Q are two concentric circular loop carrying current i 1 and i 2 as shown in figure. If ratio of their radii is 3: 2 and ratio of the flux densities at the centre O due to P and Q is 1: 3 then the value of ( i 1/ i 2) will be :- (A) (1/2) (B) (1/3) (C) (1/4) (D) (1/6)

Tardigrade Admin · Accepted Answer

(B1/B2)=(1/3) . Also, .B=(μ0 i/2 R) ⇒ ( i 1 R2/ i 2 R 1)=(1/3) ⇒ ( i 1/ i 2)=(1/3) × (3/2)=(1/2)

Q. $P$ and $Q$ are two concentric circular loop carrying current $i_{1}$ and $i_{2}$ as shown in figure. If ratio of their radii is $3 : 2$ and ratio of the flux densities at the centre $O$ due to $P$ and $Q$ is $1 : 3$ then the value of $\frac{i _{1}}{i _{2}}$ will be :-

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{1}{6}$

$\frac{B _{1}}{B _{2}} = \frac{1}{3}$
${$ Also, $B = \frac{μ _{0} i}{2 R}}$
$\Rightarrow \frac{i _{1} R _{2}}{i _{2} R _{1}} = \frac{1}{3}$
$\Rightarrow \frac{i _{1}}{i _{2}} = \frac{1}{3} \times \frac{3}{2} = \frac{1}{2}$

Q. P and Q are two concentric circular loop carrying current i1​ and i2​ as shown in figure. If ratio of their radii is 3:2 and ratio of the flux densities at the centre O due to P and Q is 1:3 then the value of i2​i1​​ will be :-

21​

31​

41​

61​