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What is the necessary condition for unstable equilibrium fo current carrying loop placed in uniform magnetic field?

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 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 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:

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

)

EASY

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

Explain the significance of a radial magnetic field when a current carrying coil is kept in it.

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

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 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 compass needle oscillates $20$ times per minute at a place where the dip is $30^{o}$ and $30$ times per minute where the dip is $60^{o}$ . The ratio of total magnetic field due to the earth at two places respectively is $\frac{4}{\sqrt{x}}$ . The value of $x$ is

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

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 coil with magnetic moment

1.5 {Am}^{2}

is oriented initially with its magnetic moment antiparallel to the direction of a uniform magnetic field of strength

0.8 T

. The amount of work done in rotating it such that the coil comes to its most stable position in the magnetic field is

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

MEDIUM

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

A bar magnet having a magnetic moment of

2.0 \times 10^{5} J T^{- 1}

, is placed along the direction of uniform magnetic field of magnitude

B = 14 \times 10^{- 5} T

. The work done in rotating the magnet slowly through

60 °

from the direction of field 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

A bar magnet with a magnetic moment

5.0 A m^{2}

is placed in parallel position relative to a magnetic field of

0.4 T

. The amount of required work done in turning the magnet form parallel to antiparallel position relative to the field direction is ________.

EASY

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

The magnetic moment of electron due to orbital motion is proportional to (

n

= principal quantum numbers)

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:

MEDIUM

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 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

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?

What is the necessary condition for unstable equilibrium fo current carrying loop placed in uniform magnetic field?

Important Questions on Magnetic Fields due to Electric Current

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