### Magnetic Effects Of Current Question 14

#### Question 14 - 30 January - Shift 1

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)

(1) $2 N_A I_A=N_B I_B$

(2) $N_A=2 N_B$

(3) $N_A I_A=4 N_B I_B$

(4) $4 N_A I_A=N_B I_B$

## Show Answer

#### Answer: (3)

#### Solution:

#### Formula: Magnetic Moment Of A Current Carrying Loop

$M=NIA$

$M_A=M_B$

$\therefore \quad N_A I_A A_A=N_B I_B A_B$

$\therefore \quad N_A I_A \pi(0.1)^{2}=N_B I_B \pi(0.2)^{2}$

$\therefore \quad N_A I_A=4 N_B I_B$