The magnetic moments associated with two closely wound circular coils A and B of radius r A =10 cm and r B=20 cm respectively are equal if: (Where N A, I A and N B, I B are number of turn and current of A and B respectively)

Question

The magnetic moments associated with two closely wound circular coils A and B of radius r A =10 cm and r B=20 cm respectively are equal if: (Where N A, I A and N B, I B are number of turn and current of A and B respectively) (A) 2 N A I A = N B I B  (B) N A =2 N B  (C) N A I A =4 N B I B  (D) 4 N A I A = N B I B

Tardigrade Admin · Accepted Answer

Sol. M = NIA M A = M B ∴ N A I A A A = N B I B A B ∴ N A I A π(0.1)2= N B I B π(0.2)2 ∴ N A I A =4 N B I B

Q. The magnetic moments associated with two closely wound circular coils $A$ and $B$ of radius $r_{A} = 10$ $c m$ and $r_{B} = 20 c m$ respectively are equal if : (Where $N_{A}, I_{A}$ and $N_{B}, I_{B}$ are number of turn and current of $A$ and $B$ respectively)

$2 N_{A} I_{A} = N_{B} I_{B}$

$N_{A} = 2 N_{B}$

$N_{A} I_{A} = 4 N_{B} I_{B}$

$4 N_{A} I_{A} = N_{B} I_{B}$

Sol. $M =$ NIA
$M_{A} = M_{B}$
$∴ N_{A} I_{A} A_{A} = N_{B} I_{B} A_{B}$
$∴ N_{A} I_{A} π (0.1)^{2} = N_{B} I_{B} π (0.2)^{2}$
$∴ N_{A} I_{A} = 4 N_{B} I_{B}$

Q. The magnetic moments associated with two closely wound circular coils A and B of radius rA​=10 cm and rB​=20cm respectively are equal if : (Where NA​,IA​ and NB​,IB​ are number of turn and current of A and B respectively)

2NA​IA​=NB​IB​

NA​=2NB​

NA​IA​=4NB​IB​

4NA​IA​=NB​IB​