The magnetic moments associated with two closely wound circular coils $A$ and $B$ of radius $r_{A}=10 \mathrm{~cm}$ and $r_{B}=20 \mathrm{~cm}$ respectively are equal if: (Where $\mathrm{N}_{\mathrm{A}}, \mathrm{I}_{\mathrm{A}}$ and $\mathrm{N}_{\mathrm{B}}, \mathrm{I}_{\mathrm{B}}$ are number of turn and current of A and B respectively)

(C) $N_{A} I_{A}=4 N_{B} I_{B}$

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

(B) $\mathrm{N}_{\mathrm{A}}=2 \mathrm{~N}_{\mathrm{B}}$

(D) $4 \mathrm{~N}_{\mathrm{A}} \mathrm{I}_{\mathrm{A}}=\mathrm{N}_{\mathrm{B}} \mathrm{I}_{\mathrm{B}}$

JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Magnetic Effects of Current

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) $N_{A} I_{A} = 4 N_{B} I_{B}$ ✓ Correct
(D) $4 N_{A} I_{A} = N_{B} I_{B}$

Answer: (C)

Solution

Equal magnetic moments require

N_{A} I_{A} π r_{A}^{2} = N_{B} I_{B} π r_{B}^{2}

. With

r_{A} = 10 cm

and

r_{B} = 20 cm

the areas are in the ratio

1 : 4

, so

N_{A} I_{A} (0.1)^{2} = N_{B} I_{B} (0.2)^{2}

reduces to

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

JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Single correct option

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