EASY

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A rectangular current loop EFGH is placed in uniform magnetic field, as shown the figure. When torque will be (i) maximum (ii) zero.

Important Questions on Magnetic Fields due to Electric Current

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Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

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 A m^{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 the coil acquires after rotating by

60^{o}

will be :

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

A magnet of total magnetic moment

10^{- 2} \hat{i} A m^{2}

is placed in a time varying magnetic field,

B \hat{i} (\cos ω t)

where

B = 1

Tesla and

ω = 0.125 rad s^{- 1}

. The work done for reversing the direction of the magnetic moment at

t = 1

second, is:

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

A coil of $50$ turns carrying a current of $2 A$ in a magnetic field of $0.5 T$ . The torque acting on the coil is

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EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

A magnetic dipole of moment

\vec{m}

is placed in the magnetic field

\vec{B}

. It is free to rotate about an axis about which its moment of inertia is

I

. It is displaced by a small angle

θ_{0} (θ_{0} < < 1)

at time

t = 0 s

and released. The dipole undergoes simple harmonic motion with angular frequency

ω

. Its potential energy at time

t

is : (Assume

\sin (α) \approx α, \cos (α) \approx 1 - \frac{α^{2}}{2}

α < < 1

)

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by

60^{o}

W

. Now, the torque required to keep the magnet in this new position is

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

A bar magnet of magnetic moment

5 A m^{2}

is placed in a uniform magnetic induction

3 \times 10^{- 5} T .

If each pole of a magnet experiences a force of

2.5 \times 10^{- 4} N

then the magnetic length of the magnet is

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

A circular current loop of magnetic moment

M

is in an arbitrary orientation in an external uniform magnetic field

\vec{B}

. The work done to rotate the loop by

30 °

about an axis perpendicular to its plane is

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

Work done in displacing a Magnetic Dipole of magnetic moment

M

, (Bar Magnet) in Uniform Magnetic Field

B

from an angle

θ_{1}

θ_{2}

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

A magnetic dipole in a uniform magnetic field has: (Take zero potential energy when magnetic dipole is perpendicular to magnetic field)

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of

75^{o}

. One of the fields has a magnitude of

15 mT

. The dipole attains stable equilibrium at an angle of

30^{o}

with this field. The magnitude of the other field (in

mT

) is close to

HARD

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

A beam of neutrons performs circular motion of radius,

r = 1 m,

under the influence of an inhomogeneous magnetic field with inhomogeneity extending over

Δ r = 0.01 m .

The speed of the neutrons is

54 {ms}^{- 1} .

The mass and magnetic moment of the neutrons respectively are

1.67 \times 10^{- 27} kg

and

9.67 \times 10^{- 27} J / T .

The average variation of the magnetic field over

Δ r

is approximately.

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

A rectangular coil of length

0.12 m

and width

0.1 m

having

50

turns of wire is suspended vertically in a uniform magnetic field of strength

0.2

W e b e r / m^{2}

. The coil carries a current of

2 A

. If the plane of the coil is inclined at an angle of

30^{o}

with the direction of the field, the torque required to keep coil in stable equilibrium will be:

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

A bar magnet is held perpendicular to uniform magnetic field. The torque acting on the magnet is to be made half by rotating it. It should be rotated through an angle

(\sin 30 ° = 0.5, \sin 90 ° = 1)

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

A coil in the shape of an equilateral triangle of side

l

is suspended between the pole pieces of a permanent magnet such that

B

is in plane of the coil. If due to a current

i

in the triangle, a torque

τ

rests on it, the side

l

of the triangle is

HARD

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

In a uniform magnetic field, the magnetic needle has a magnetic moment

9.85 \times 10^{- 2} A m^{- 2}

and moment of inertia

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

If it performs

10

complete oscillations in

5

seconds then the magnitude of the magnetic field is ____

mT

[Take

π^{2}

9.85]

EASY

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

The rectangular coil of area $A$ is in a field $B .$ Find the torque about the $Z$ -axis when the coil lies in the position shown and carries a current $I .$

Question Image

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

Two short magnetic dipoles $m_{1}$ and $m_{2}$ each having magnetic moment of $1 A m^{2}$ are placed at point $O$ and $P$ respectively. The distance between $O P$ is $1 m$ . The torque experienced by the magnetic dipole $m_{2}$ due to the presence of $m_{1}$ is $________\times 10^{- 7} N m$ .

Question Image

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

A magnetic needle has a magnetic moment of

5 \times 10^{- 2} {Am}^{2}

and moment of inertia

8 \times 10^{- 6} {kgm}^{2}

. It has a period of oscillation of

2 s

in a magnetic field

\vec{B}

. The magnitude of magnetic field is approximately;

MEDIUM

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

A magnetic dipole is placed in a uniform magnetic field of intensity

B

, oriented along the direction of the field. If the magnetic dipole moment is

M

, then the maximum work an external agent can perform in rotating the dipole will be

HARD

Physics>Electricity and Magnetism>Magnetic Fields due to Electric Current>Torque on Current Loop, Magnetic Dipole

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 figure below.
(a) Question Image (b)

(c) (d)

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 rectangular current loop EFGH is placed in uniform magnetic field, as shown the figure. When torque will be (i) maximum (ii) zero.

Important Questions on Magnetic Fields due to Electric Current

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