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How do you find the magnetic dipole moment?

Important Questions on Properties of Magnets and Terrestrial Magnetism

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Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

The ratio of magnetic fields due to a bar magnet at the two axial points

P_{1}

and

P_{2}

which are separated from each other by

10 cm

25 : 2

P_{1}

Point is situated at

10 cm

from the centre of the magnet. (Points

P_{1}

and

P_{2}

are on the same side of magnet and distance of

P_{1}

and

P_{2}

from the centre of magnet is much greater than the distance of two ends of the magnet from the centre). Magnetic length of the bar magnet is

EASY

Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

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>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

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]

MEDIUM

Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

A bar magnet of magnetic moment $M$ is placed at a distance $D$ with its axis along positive $X$ -axis. Likewise, second bar magnet of magnetic moment $M$ is placed at a distance $2 D$ on positive $Y$ -axis and perpendicular to it as shown in the figure. The magnitude of magnetic field at the origin is $|\vec{B}| = α [\frac{μ_{0}}{4 π} \frac{M}{D^{3}}]$ . The value of $α$ must be (Assume $D > >$ where $l$ is the length of magnets)

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MEDIUM

Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

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:

EASY

Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

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>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

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>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

A steel wire of length

l

has a magnetic moment

M

. It is then bent into a semicircular arc. The new magnetic moment is

HARD

Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

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>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

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>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

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:

EASY

Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

Which of the following statements are correct?
(A) Electric monopoles do not exist whereas magnetic monopoles exist.
(B) Magnetic field lines due to a solenoid at its ends and outside cannot be completely straight and confined.
(C) Magnetic field lines are completely confined within a toroid.
(D) Magnetic field lines inside a bar magnet are not parallel.
(E) $χ = - 1$ is the condition for a perfect diamagnetic material, where $χ$ is its magnetic susceptibility.

Choose the correct answer from the options given below :

MEDIUM

Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

Consider a magnetic dipole kept in the north to south direction. Let

P_{1}, P_{2}, Q_{1}, Q_{2}

be four points at the same distance from the dipole towards north, south, east and west of the dipole respectively. The directions of the magnetic field due to the dipole are the same at the directions of the magnetic field due to the dipole are opposite at

EASY

Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

Two identical thin bar magnets each of length

l

and pole strength

m

are placed at right angles to each other with north-pole of one touching south-pole of the other, then the magnetic moment of the system is

MEDIUM

Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

Sketch the magnetic field lines for a current-carrying circular loop near its centre. Replace the loop by an equivalent magnetic dipole and sketch the magnetic field lines near the centre of the dipole. Identify the difference.

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Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

Two/three/four identical bar magnets of magnetic moment $M$ are combined according to figure. Find the net magnetic moment of the system.

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MEDIUM

Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

A bar magnet of length

3 cm

has a point

A

and

B

along axis at a distance of

24 cm

and

48 cm

on the opposite ends. Ratio of magnetic fields at these points will be?

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EASY

Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

Calculate the magnetic moment of a closely wound coil of

200

turns having a radius

15 cm

and carrying a current of

4 A

EASY

Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

Assertion : A linear solenoid carrying current is equivalent to a bar magnet.
Reason : The magnetic field lines due to current carrying solenoid resemble exactly with those of a bar magnet

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Physics>Electricity and Magnetism>Properties of Magnets and Terrestrial Magnetism>Magnet as a Dipole

A bar magnet is oscillating in the Earth's magnetic field with time period

T

. If its mass is increased four times, then its time period will be

How do you find the magnetic dipole moment?

Important Questions on Properties of Magnets and Terrestrial Magnetism

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