# Physics Class 12 NCERT Solutions: Chapter 5 Magnetism and Matter Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Q: 7. A bar magnet of magnetic moment lies aligned with the direction of a uniform magnetic field of .

(A) What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment: (i) normal to the field direction, (ii) opposite to the field direction?

(B) What is the torque on the magnet in cases (i) and (ii) ?

(A) Magnetic moment,

Magnetic field strength,

(i) Initial angle between the axis and the magnetic field,

Final angle between the axis and the magnetic field,

The work required to make the magnetic moment normal to the direction of magnetic field is given as:

(ii) Initial angle between the axis and the magnetic field,

Final angle between the axis and the magnetic field,

The work required to make the magnetic moment opposite to the direction of magnetic field is given as:

(B) For case (i) :

∴ Torque,

For case (ii) :

∴ Torque,

Q: 8. A closely wound solenoid of turns and area of cross-section, , carrying a current of , is suspended through its centre allowing it to turn in a horizontal plane.

(A) What is the magnetic moment associated with the solenoid?

(B) What is the force and torque on the solenoid if a uniform horizontal magnetic field of is set up at an angle of with the axis of the solenoid?

Number of turns on the solenoid,

Area of cross-section of the solenoid,

Current in the solenoid,

(a) The magnetic moment along the axis of the solenoid is calculated as:

(B) Magnetic field,

Angle between the magnetic field and the axis of the solenoid,

Torque,

Since the magnetic field is uniform, the force on the solenoid is zero. The torque on the solenoid is

Q: 9. A circular coil of turns and radius carrying a current of rests with its plane normal to an external field of magnitude . The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a frequency of . What is the moment of inertia of the coil about its axis of rotation?

Number of turns in the circular coil,

Cross-section of the coil,

Current in the coil,

Magnetic field strength,

Frequency of oscillations of the coil,

∴ Magnetic moment,

Frequency is given by the relation:

Where,

I = Moment of inertia of the coil

Hence, the moment of inertia of the coil about its axis of rotation is

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