# Physics Class 12 NCERT Solutions: Chapter 5 Magnetism and Matter Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Q: 3. A short bar magnet placed with its axis at with a uniform external magnetic field of experiences a torque of magnitude equal to. What is the magnitude of magnetic moment of the magnet?

Magnetic field strength,

Torque on the bar magnet,

Angle between the bar magnet and the external magnetic field,

Torque is related to magnetic moment (M) as:

Hence, the magnetic moment of the magnet is .

Q: 4. A short bar magnet of magnetic moment is placed in a uniform magnetic field of . If the bar is free to rotate in the plane of the field, which orientation would correspond to its (a) stable, and (b) unstable equilibrium? What is the potential energy of the magnet in each case?

Moment of the bar magnet,

External magnetic field,

(A) The bar magnet is aligned along the magnetic field. This system is considered as being in stable equilibrium. Hence, the angle , between the bar magnet and the magnetic field is .

Potential energy of the system

(B) The bar magnet is oriented to the magnetic field. Hence, it is in unstable equilibrium.

Potential energy

Q: 5. A closely wound solenoid of turns and area of cross section carries a current of . Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?

Number of turns in the solenoid,

Area of cross-section,

Current in the solenoid,

A current-carrying solenoid behaves as a bar magnet because a magnetic field develops along its axis, i.e.. , along its length.

The magnetic moment associated with the given current-carrying solenoid is calculated as:

Q: 6. If the solenoid in Exercise is free to turn about the vertical direction and a uniform horizontal magnetic field of is applied, what is the magnitude of torque on the solenoid when its axis makes an angle of 30° with the direction of applied field?