More about Magnetic Dipoles

Q. A magnet of moment $4.0$ ${\text{Am}}^2$ is held in a uniform magnetic field $5.0\times {10}^{-4}$ Tesla with the magnetic moment vector making an angle of ${30}^{\circ }$ with the field. The work done in increasing the angle from ${30}^{\circ }\text{to}{45}^{\circ }$ is nearly

1. $3.18\times {10}^{-4}\text{J}$
2. $4.3\times {10}^{-4}\text{J}$
3. $7.3\times {10}^{-4}\text{J}$
4. Zero

Q. Two short bar magnets of magnetic moments $‘M^{\prime }$ each are arranged at the opposite corners of a square of side $‘d^{\prime }$ such that their centres coincide with the corners and their axes are parallel to one side of the square. If the like poles are in the same direction, the magnetic induction at any of the other corners of the square is.

1. $\frac{{\mu }_{o}M}{4\pi d^3}$
2. $\frac{{\mu }_{o}2M}{4\pi d^3}$
3. $\frac{{\mu }_{o}M}{2\pi d^3}$
4. $\frac{{\mu }_{o}2M}{2\pi d^3}$

Q.

A circular coil of radius 4 cm and of 20 turns carries a current of 3 amperes. It is placed in a magnetic field of intensity of 0.5 . The magnetic dipole moment of the coil is

1. 

2. 

3. 

4. 

Q. Magnitude of magnetic dipole moment of loop as shown in figure is? Each curve is of radius R.

1. $\pi R^{2}i$
2. $2\pi R^{2}i$
3. $\frac{\pi R^{2}i}{2}$
4. $\frac{3}{4}\pi R^{2}i$

Q. A circular coil of radius 4 cm and 20 turns carries a current of 3 ampere. It is placed in a magnetic field of 0.5 T. The magnitude of magnetic dipole moment of the coil will be?

1. $0.60A-m^2$
2. $0.45A-m^2$
3. $0.3A-m^2$
4. $0.15A-m^2$

Q. A circular coil of radius 4 cm has 50 turns. In this coil a current of 2 A is flowing. It is placed in a magnetic field of $0.1weber/m^2$. The amount of work done in rotating it through ${180}^{\circ }$ from its equilibrium position will be

1. 0.1 J
2. 0.2 J
3. 0.5 J
4. 0.8 J

Q. An insulating rod of length L carries a charge $q$ distributed uniformly on it. The rod is pivoted at its mid-point and is rotated at a frequency f about a fixed axis perpendicular to the rod and passing through the pivot. The magnetic moment of the rod system is

1. $\frac{1}{12}\pi qf{l}^2$
2. $\pi qf{l}^2$
3. $\frac{1}{6}\pi qf{l}^2$
4. $\frac{1}{3}\pi qf{l}^2$

Q.

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle, of ${75}^{\circ }$. One of the fields has a magnitude of $\sqrt{2}\times {10}^{-2}T$. The dipole attains stable equilibrium at an angle of ${30}^{\circ }$ with this field. What is the magnitude of the other field?

1. 0.01 T

2. 0.02 T

3. 0.03 T

4. 0.04 T

Q. An insulating rod of length $l$ carries a charge $q$ distributed uniformly on it. The rod is pivoted at its mid-point and is rotated at a frequency $f$ about a fixed axis perpendicular to the rod and passing through the pivot. The magnetic moment of the rod system is

1. $\frac{1}{12}\pi qf{l}^2$
2. $\pi qf{l}^2$
3. $\frac{1}{6}\pi qf{l}^2$
4. $\frac{1}{3}\pi qf{l}^2$

Q. The magnetic moment of an electron (charge = -e, mass = m) moving in a circular orbit of radius r with speed v about a nucleus of mass M is proportional to

1. mr
2. vr
3. evr
4. Mvr

Q. A semicircular ring of radius R uniformly charged with chage Q is rotated with angular velocity $\omega$ about point P as shown in figure. Its magnetic dipole moment will be.

1. $\frac{Qw{R}^2}{4}$
2. $\frac{Qw{R}^2}{3}$
3. $\frac{Qw{R}^2}{2}$
4. $Q\omega R^2$

Q. An insulating rod of length $l$ carries a charge $q$ distributed uniformly on it. The rod is pivoted at its mid-point and is rotated at a frequency $f$ about a fixed axis perpendicular to the rod and passing through the pivot. The magnetic moment of the rod system is

1. $\frac{1}{12}\pi qf{l}^2$
2. $\pi qf{l}^2$
3. $\frac{1}{6}\pi qf{l}^2$
4. $\frac{1}{3}\pi qf{l}^2$

Q. 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 $60°$ is $W$. Now the torque required to keep the magnet in this new position is

1. $\frac{\sqrt{3}W}{2}$
2. $\frac{2W}{\sqrt{3}}$
3. $\frac{W}{\sqrt{3}}$
4. $\sqrt{3}W$