(C) The magnetic moment $M$ of a circular coil is given by the formula $M = NIA$,where $N$ is the number of turns,$I$ is the current,and $A$ is the ar

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(C) The magnetic moment $M$ of a circular coil is given by the formula $M = NIA$,where $N$ is the number of turns,$I$ is the current,and $A$ is the area of the coil.Given that the magnetic moments of coils $A$ and $B$ are equal,we have $M_A = M_B$.Substituting the formula,we get $N_A I_A A_A = N_B I_B A_B$.The area of a circular coil is $A = \pi r^2$. Thus,$A_A = \pi (r_A)^2$ and $A_B = \pi (r_B)^2$.Substituting the values $r_A = 10 \ cm = 0.1 \ m$ and $r_B = 20 \ cm = 0.2 \ m$:$N_A I_A \pi (0.1)^2 = N_B I_B \pi (0.2)^2$$N_A I_A (0.01) = N_B I_B (0.04)$Dividing both sides by $0.01$,we get $N_A I_A = 4 N_B I_B$.

Class 12 Physics Moving Charges and Magnetism Magnetic Moment of Current Carrying Coil

Medium

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 the number of turns and current of $A$ and $B$ respectively)

JEE MAIN 2023 All JEE MAIN

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
$4 N_A I_A = N_B I_B$

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Magnetic Moment of Current Carrying Coil

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An insulated wire is wound so that it forms a flat coil with $N = 200$ turns. The radius of the innermost turn is $r_1 = 3\text{ cm}$,and of the outermost turn $r_2 = 6\text{ cm}$. If $20\text{ mA}$ current flows in it,then the magnetic moment will be $\alpha \times 10^{-2}\text{ A.m}^2$. The value of $\alpha$ is . . . . . . .

DifficultJEE MAIN 2026

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$A$ current of $3 \, A$ is flowing in a plane circular coil of radius $4 \, cm$ and number of turns $20$. The coil is placed in a uniform magnetic field of magnetic induction $0.5 \, T$. The magnetic dipole moment of the coil is $... \, A \cdot m^2$.

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$A$ circular coil and a square coil are prepared from two identical metal wires,and the same current is passed through them. The ratio of the magnetic dipole moment associated with the circular coil to that of the square coil is:

DifficultMHT CET 2019

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The magnetic field at the centre of a current carrying circular coil of area $A$ is $B$. The magnetic moment $(M)$ of the coil is $(\mu_0 = \text{permeability of free space})$

MediumMHT CET 2025

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$A$ coil carrying a heavy current and having a large number of turns is mounted in a $N-S$ vertical plane,and a current flows in a clockwise direction. $A$ small magnetic needle at its center will have its north pole in:

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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 the number of turns and current of $A$ and $B$ respectively)

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$A$ current of $3 \, A$ is flowing in a plane circular coil of radius $4 \, cm$ and number of turns $20$. The coil is placed in a uniform magnetic field of magnetic induction $0.5 \, T$. The magnetic dipole moment of the coil is $... \, A \cdot m^2$.

$A$ circular coil and a square coil are prepared from two identical metal wires,and the same current is passed through them. The ratio of the magnetic dipole moment associated with the circular coil to that of the square coil is:

The magnetic field at the centre of a current carrying circular coil of area $A$ is $B$. The magnetic moment $(M)$ of the coil is $(\mu_0 = \text{permeability of free space})$

$A$ coil carrying a heavy current and having a large number of turns is mounted in a $N-S$ vertical plane,and a current flows in a clockwise direction. $A$ small magnetic needle at its center will have its north pole in:

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