Q79 / 90 · JEE Main 2023 (30 Jan Shift 1) · Physics

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
$N_{A} = 2 N_{B}$
Correct answer
C
$N_{A} I_{A} = 4 N_{B} I_{B}$
D
$4 N_{A} I_{A} = N_{B} I_{B}$

Solution

As magnetic moment of both the coil is the same,

$μ_{1} = μ_{2}$

$\Rightarrow N_{A} [I_{A} π (r_{A}^{2})] = N_{B} [I_{B} π {(r_{B}^{2})}^{2}] \Rightarrow N_{A} [I_{A} {(0.10)}^{2}] = N_{B} [I_{B} {(0.20)}^{2}] \Rightarrow I_{A} N_{A} = 4 I_{B} N_{B}$

Hence, the correct answer is option: 'C'.

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

Solution

Relevant Questions

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)