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A bar magnet of magnetic moment $1.5 J T^{- 1}$ lies aligned with the direction of a magnetic field of $0.22 T .$ What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment normal to the field direction?

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Important Questions on Matter and Magnetism

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Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

The magnetic field of earth at the equator is approximately

4 \times 1 0^{- 5} T

. The radius of earth is

6.4 \times 1 0^{6} m

. Then the dipole moment of the earth will be nearly of the order of :

HARD

Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

A uniform magnetic field

B

0 .3 T

is along the positive

Z

-direction. A rectangular loop (

a b c d

) of sides

10 cm \times 5 cm

carries a current

I

12 A

. Out of the following different orientations which one corresponds to stable equilibrium?

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Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

The mid points of two small magnetic dipoles of length

d

in end-on positions, are separated by a distance

x

(x ≫ d)

. The magnitude of force between them is proportional to

x^{- n}

where

n

is :

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Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

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:

HARD

Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

At some location the horizontal component of earth's magnetic field is

18 \times 10^{- 6} T .

At this location, magnetic needle of length

0.12 m

and pole strength

1.8 Am

is suspended from its mid-point using a thread, it makes

45 °

angles with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is:

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

A circular coil having

N

turns and radius

r

carries a current

I .

It is held in the

X Z

plane in a magnetic field

B \hat{i}

. The torque on the coil due to the magnetic field is:

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Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

250

-Turn rectangular coil of length

2.1 cm

and width

1.25 cm

carries a current of

85 μA

and subjected to a magnetic field of strength

0.85 T.

Work done for rotating the coil by

180 °

against the torque is:

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Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

A thin rod of length

L

is magnetized and has magnetic moment

M

. The rod is then bent in a semicircular arc. The magnetic moment in the new shape is

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Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

A magnetic needle of magnetic moment

6 .7 \times 10^{- 2} A m^{2}

and moment of inertia

7 .5 \times 10^{- 6} kg m^{2}

is performing simple harmonic oscillations in a magnetic field of

0.01 T

. Time taken for

10

complete oscillations is:

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Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

The magnetic flux near the axis and inside the air-core solenoid of length

60 cm

carrying current

I

1.57 \times 10^{6} Wb .

Its magnetic moment will be (cross-sectional area of a solenoid is very small as compared to its length,

μ_{0} = 4 π \times 10^{- 7}

SI units)

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

The magnetic dipole moment of a short magnetic dipole at a distant point along the equator of magnet has a magnitude of

X

in SI units. If the distance between point and the magnet is halved then the magnitude of dipole moment will be

HARD

Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

Two short bar magnets of length

1 cm

each have magnetic moments

1 .20 A m^{2}

and

1 .00 A m^{2}

respectively. They are placed on a horizontal table parallel to each other with their

N

poles pointing towards the south. They have a common magnetic equator and are separated by a distance of

20 .0 cm

. The value of the resultant horizontal magnetic induction at the mid-point

O

of the line joining their centres is close to
( Horizontal component of earth's magnetic induction is

3 .6 \times 10^{- 5} Wb m^{- 2}

)

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Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

An electron gun is placed inside a long solenoid of radius

R

on its axis. The solenoid has

n

turns/length and carries a current

I .

The electron gun shoots an electron along the radius of the solenoid with speed

v .

If the electron does not hit the surface of the solenoid, maximum possible value of

v

is (all symbols have their standard meaning):

Question Image

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Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

A rectangular coil (Dimension

5 c m \times 2.5 c m

) with

100

turns, carrying a current of

3 A

in the clock-wise direction, is kept centered at the origin and in the

X - Z

plane. A magnetic field of

1 T

is applied along

X - a x i s

. If the coil is tilted through

45 °

about

Z - a x i s

, then the torque on the coil is:

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Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

A small bar magnet is placed with its axis at

30^{o}

with an external magnetic field of

0.06 T

experiences a torque of

0.018 Nm

. The minimum work required to rotate it from its stable to unstable equilibrium position is:

HARD

Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

Two short bar magnets

A

and

B

(having magnetic moments

M_{1}

and

M_{2}

respectively) are kept one above the other with their magnetic axis perpendicular to each other. If their resultant at a point on the axis of magnet

A

is inclined at

45 °

with the axis of magnet

A

then the ratio of magnetic moments

\frac{M_{2}}{M_{1}}

[\tan 45 ° = 1]

EASY

Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

A magnetic needle kept in a non-uniform magnetic field, can experiences

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Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

Two identical bar magnets are held perpendicular to each other with a certain separation, as shown below. The area around the magnets is divided into four zones.
Question Image

Given that there is a neutral point it is located in,

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Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

A short bar magnet is placed in the magnetic meridian of the earth with North Pole pointing north. Neutral points are found at a distance of $30 cm$ from the magnet on the East-West line, drawn through the middle point of the magnet. The magnetic moment of the magnet in ${Am}^{2}$ is close to:

(Given $\frac{μ_{0}}{4 π} = 10^{- 7}$ in SI units and $B_{H} =$ Horizontal component of earth's magnetic field $= 3.6 \times 10^{- 5}$ Tesla.)

HARD

Physics>Electricity and Magnetism>Matter and Magnetism>Magnetic Dipole in External Magnetic Field

A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are

T_{h}

and

T_{c}

respectively, then:

A bar magnet of magnetic moment 1.5 J T-1 lies aligned with the direction of a magnetic field of 0.22 T. What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment normal to the field direction?

Important Questions on Matter and Magnetism

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A bar magnet of magnetic moment $1.5 J T^{- 1}$ lies aligned with the direction of a magnetic field of $0.22 T .$ What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment normal to the field direction?