Magnetic Moment of Current Loop

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JEE Advanced 1988

In a hydrogen atom, the electron moves in an orbit of radius $0.5 \overset{˚}{A}$ making $1 0^{16}$ revolutions per second. The magnetic moment associated with the orbital motion of the electron is ......

JEE Advanced 2012

A loop carrying current $I$ lies in the $x$ - $y$ plane as shown in the figure. The unit vector $\hat{k}$ is coming out of the plane of the paper. The magnetic moment of the current loop is

a^{2} I \hat{k}

(B)

(\frac{π}{2} + 1) a^{2} I \hat{k}

(C)

- (\frac{π}{2} + 1) a^{2} I \hat{k}

(D)

(2 π + 1) a^{2} I \hat{k}

JEE Advanced 2009

LEVELJEE Advanced

Six point charges, each of the same magnitude $q$ , are arranged in different manners as shown in Column II. In each case, a point $M$ and a line $P Q$ passing through $M$ are shown. Let $E$ be the electric field and $V$ be the electric potential at $M$ (potential at infinity is zero) due to the given charge distribution when it is at rest. Now, the whole system is set into rotation with a constant angular velocity about the line $P Q$ . Let $B$ be the magnetic field at $M$ and $μ$ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current.

List-I

(P)

E = 0

(Q)

V \neq = 0

(R)

B = 0

(S)

μ \neq = 0

List-II

(1)

Charges are at the corners of a regular hexagon.

M

is at the centre of the hexagon.

P Q

is perpendicular to the plane of the hexagon.

(2)

Charges are on a line perpendicular to

P Q

at equal intervals.

M

is the mid-point between the two innermost charges.

(3)

Charges are placed on two coplanar insulating rings at equal intervals.

M

is the common centre of the rings.

P Q

is perpendicular to the plane of the rings.

(4)

Charges are placed at the corners of a rectangle of sides

a

and

2 a

and at the mid points of the longer sides.

M

is at the centre of the rectangle.

P Q

is parallel to the longer sides.

(5)

Charges are placed on two coplanar, identical insulating rings at equal intervals.

M

is the mid points between the centres of the rings.

P Q

is perpendicular to the line joining the centres and coplanar to the rings.

JEE Advanced 1987

LEVELBoard

A wire of length $L$ metre carrying a current $i$ ampere is bent in the form of circle. The magnitude of its magnetic moment is ...... in MKS units.

JEE Main 2003

LEVELJEE Main

A current carrying loop is placed in a uniform magnetic field in four different orientations, I, II, III and IV. Arrange them in the decreasing order of potential energy.

An electron in the ground state of hydrogen atom is revolving in anti-clockwise direction in a circular orbit of radius $R$ . (a) Obtain an expression for the orbital magnetic moment of the electron. (b) The atom is placed in a uniform magnetic induction $B$ such that the normal to the plane of electron's orbit makes an angle of $3 0^{\circ}$ with the magnetic induction. Find the torque experienced by the orbiting electron.

JEE Advanced 2002

LEVELJEE Advanced

A rectangular loop PQRS made from a uniform wire has length a, width b and mass m. It is free to rotate about the arm PQ, which remains hinged along a horizontal line taken as the y-axis (see figure). Take the vertically upward direction as the z-axis. A uniform magnetic field $B = (3 \hat{i} + 4 \hat{k}) B_{0}$ exists in the region. The loop is held in the x-y plane and a current I is passed through it. The loop is now released and is found to stay in the horizontal position in equilibrium. (a) What is the direction of the current I in PQ ? (b) Find the magnetic force on the arm RS. (c) Find the expression for I in terms of $B_{0}$ , a, b and m

LEVELJEE Main

A particle of charge $q$ and mass $m$ moves in a circular orbit of radius $r$ with angular speed $ω$ . The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

(A)

ω

and

q

(B)

ω

q

and

m

(C)

q

and

m

(D)

ω

and

m

LEVELJEE Main

Two particles, each of mass $m$ and charge $q$ , are attached to the two ends of a light rigid rod of length $2 R$ . The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is

(A)

\frac{q}{2 m}

(B)

\frac{q}{m}

(C)

\frac{2 q}{m}

(D)

\frac{q}{π m}

JEE Advanced 1998

LEVELJEE Advanced

A uniform constant magnetic field $B$ is directed at an angle of $4 5^{\circ}$ to the $x$ -axis in $x$ - $y$ plane. $P QR S$ is rigid square wire frame carrying a steady current $I_{0}$ , with its centre at the origin $O$ . At time $t = 0$ , the frame is at rest in the position shown in the figure with its sides parallel to $x$ and $y$ -axes. Each side of the frame is of mass $M$ and length $L$ . (1998) (a) What is the magnitude of torque $τ$ acting on the frame due to the magnetic field ? (b) Find the angle by which the frame rotates under the action of this torque in a short interval of time $Δ t$ and the axis about which this rotation occurs ( $Δ t$ is so short that any variation in the torque during this interval may be neglected). Given : the moment of inertia of the frame about an axis through its centre perpendicular to its plane is $\frac{4}{3} M L^{2}$ .

JEE Advanced 2025

LEVELJEE Advanced

A conducting solid sphere of radius $R$ and mass $M$ carries a charge $Q$ . The sphere is rotating about an axis passing through its center with a uniform angular speed $ω$ . The ratio of the magnitudes of the magnetic dipole moment to the angular momentum about the same axis is given as $α \frac{Q}{2 M}$ . The value of $α$ is _______.

JEE Advanced 2024

LEVELJEE Advanced

A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass $m$ and radius $r$ and it is in a uniform vertical magnetic field $B_{0}$ , as shown in the figure. Initially, it hangs vertically downwards, because of acceleration due to gravity $g$ , on two conducting supports at $P$ and $Q$ . When a current $I$ is passed through the loop, the loop turns about the line $P Q$ by an angle $θ$ given by

(A)

tan θ = \frac{π r I B _{0}}{m g}

(B)

tan θ = \frac{2 π r I B _{0}}{m g}

(C)

tan θ = \frac{π r I B _{0}}{2 m g}

(D)

tan θ = \frac{m g}{π r I B _{0}}

JEE Advanced 2026

LEVELJEE Advanced

A hollow, right circular cone of base radius $R$ and height $h$ , with its tip at the origin is rotating about the Z-axis with an angular velocity $ω$ , as shown in the figure. The cone carries a total charge $Q$ uniformly distributed on its curved surface. The magnitude of magnetic field at a point $(0, 0, z)$ , where $z ≫ R$ and $z ≫ h$ , is $\frac{n μ _{0} Q R ^{2} ω}{4 π z ^{3}}$ . The value of $n$ is:

JEE Advanced 2020

LEVELJEE Advanced

A circular coil of radius $R$ and $N$ turns has negligible resistance. As shown in the schematic figure, its two ends are connected to two wires and it is hanging by those wires with its plane being vertical. The wires are connected to a capacitor with charge $Q$ through a switch. The coil is in a horizontal uniform magnetic field $B_{o}$ parallel to the plane of the coil. When the switch is closed, the capacitor gets discharged through the coil in a very short time. By the time the capacitor is discharged fully, magnitude of the angular momentum gained by the coil will be (assume that the discharge time is so short that the coil has hardly rotated during this time)-

(A)

\frac{π}{2} N Q B_{o} R^{2}

(B)

π N Q B_{o} R^{2}

(C)

2 π N Q B_{o} R^{2}

(D)

4 π N Q B_{o} R^{2}

JEE Main 2018

LEVELJEE Main

The dipole moment of a circular loop carrying a current $I$ , is $m$ and the magnetic field at the centre of the loop is $B_{1}$ . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_{2}$ . The ratio $\frac{B _{1}}{B _{2}}$ is

(A)

2

(B)

3

(C)

2

(D)

\frac{1}{2}

JEE Main 2020

LEVELJEE Advanced

A wire carrying current $I$ is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths $a$ and $b$ , then the magnitude and direction of magnetic moment of the loop ABCDEFA is

(A)

ab I

, along

(\frac{j ^}{2} + \frac{k ^}{2})

(B)

2 ab I

, along

(\frac{j ^}{2} + \frac{k ^}{2})

(C)

2 ab I

, along

(\frac{j ^}{5} + \frac{2 k ^}{5})

(D)

ab I

, along

(\frac{j ^}{5} + \frac{2 k ^}{5})

JEE Main 2020

LEVELJEE Advanced

A circular coil has moment of inertia $0.8 kg m^{2}$ around any diameter and is carrying current to produce a magnetic moment of $20 Am^{2}$ . The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of $4 T$ is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed of the coil, acquired after rotating by $6 0^{\circ}$ , will be

(A)

10 rad s^{- 1}

(B)

20 π rad s^{- 1}

(C)

10 π rad s^{- 1}

(D)

20 rad s^{- 1}

JEE Main 2015

LEVELJEE Main

A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientations as shown in the figures below. If there is a uniform magnetic field of 0.3 T in the positive z-direction in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium?

(A)

(a) and (b) respectively

(B)

(a) and (c) respectively

(C)

(b) and (d) respectively

(D)

(b) and (c) respectively

JEE Main 2019

LEVELJEE Advanced

An insulating thin rod of length $l$ has a linear charge density $ρ (x) = ρ_{0} \frac{x}{l}$ on it. The rod is rotated about an axis passing through the origin ( $x = 0$ ) and perpendicular to the rod. If the rod makes $n$ rotations per second, then the time averaged magnetic moment of the rod is

(A)

n ρ l^{3}

(B)

π n ρ l^{3}

(C)

\frac{π}{3} n ρ l^{3}

(D)

\frac{π}{4} n ρ l^{3}

JEE Main 2019

LEVELJEE Advanced

An infinitely long current-carrying wire and a small current-carrying loop are in the plane of the paper as shown. The radius of the loop is $a$ and distance of its centre from the wire is $d$ ( $d >> a$ ). If the loop applies a force $F$ on the wire, then

(A)

F \propto (\frac{a ^{2}}{d ^{3}})

(B)

F = 0

(C)

F \propto (\frac{a}{d})

(D)

F \propto (\frac{a}{d})^{2}

LEVELJEE Advanced

A thin circular disk of radius $R$ is uniformly charged with density $σ > 0$ per unit area. The disk rotates about its axis with a uniform angular speed $ω$ . The magnetic moment of the disk is

(A)

2 π R^{4} σ ω

(B)

π R^{4} σ ω

(C)

\frac{π R ^{4}}{2} σ ω

(D)

\frac{π R ^{4}}{4} σ ω

JEE Main 2020

LEVELJEE Main

A small circular loop of conducting wire has radius $a$ and carries current $i$ . It is placed in a uniform magnetic field $B$ perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period $T$ . If the mass of the loop is $m$ , then

(A)

T = \frac{π m}{i B}

(B)

T = \frac{2 m}{i B}

(C)

T = \frac{2 π m}{i B}

(D)

T = \frac{π m}{2 i B}

JEE Main 2021

LEVELJEE Main

A uniform conducting wire of length is $24 a$ , and resistance $R$ is wound up as a current carrying coil in the shape of an equilateral triangle of side $a$ and then in the form of a square of side $a$ . The coil is connected to a voltage source $V_{0}$ . The ratio of magnetic moment of the coils in case of equilateral triangle to that for square is $1 : y$ . The value of where $y$ is ......... .

JEE Main 2020

LEVELJEE Advanced

A charged particle going around in a circle can be considered to be a current loop. A particle of mass $m$ carrying charge $q$ is moving in a plane with speed $v$ under the influence of magnetic field $B$ . The magnetic moment of this moving particle

(A)

\frac{m v ^{2} B}{2 B ^{2}}

(B)

- \frac{m v ^{2} B}{2 π B ^{2}}

(C)

- \frac{m v ^{2} B}{B ^{2}}

(D)

- \frac{m v ^{2} B}{2 B ^{2}}

JEE Main 2019

LEVELJEE Main

A circular coil having $N$ turns and radius $r$ carries a current $I$ . It is held in the XZ-plane in a magnetic field $B \hat{i}$ . The torque on the coil due to the magnetic field (in N-m) is

(A)

\frac{B r ^{2} I}{π N}

(B)

B π r^{2} I N

(C)

\frac{B π r ^{2} I}{N}

(D)

Zero

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A loop carrying current I lies in the x-y plane as shown in the figure. The unit vector k^ is coming out of the plane of the paper. The magnetic moment of the current loop is

List-I

List-II

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A wire of length L metre carrying a current i ampere is bent in the form of circle. The magnitude of its magnetic moment is ...... in MKS units.

A current carrying loop is placed in a uniform magnetic field in four different orientations, I, II, III and IV. Arrange them in the decreasing order of potential energy.

A loop carrying current $I$ lies in the $x$ - $y$ plane as shown in the figure. The unit vector $\hat{k}$ is coming out of the plane of the paper. The magnetic moment of the current loop is

A wire of length $L$ metre carrying a current $i$ ampere is bent in the form of circle. The magnitude of its magnetic moment is ...... in MKS units.