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Two bar magnets of the same mass, same length and breadth but having magnetic moments $M$ and $2 M$ are joined together pole for pole and suspended by a string.

The time period of assembly in a magnetic field of strength $H$ is $3 s$ . If now the polarity of one of the magnets is reversed and the combination is again made to oscillate in the same field, the time of oscillation is

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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

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:

MEDIUM

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:

MEDIUM

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 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:

MEDIUM

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

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:

MEDIUM

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 :

MEDIUM

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

HARD

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)

MEDIUM

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

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}

)

HARD

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

MEDIUM

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]

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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

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?

MEDIUM

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

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:

Important Questions on Matter and Magnetism

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