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. $4 N _{ A } I _{ A }= N _{ B } I _{ B }$

Answer 1

Answer: (C)

Sol. $M =$ NIA
$ M _{ A }= M _{ B } $
$\therefore N _{ A } I _{ A } A _{ A }= N _{ B } I _{ B } A _{ B } $
$\therefore N _{ A } I _{ A } \pi(0.1)^2= N _{ B } I _{ B } \pi(0.2)^2 $
$\therefore N _{ A } I _{ A }=4 N _{ B } I _{ B }$