# Physics Class 12 NCERT Solutions: Chapter 5 Magnetism and Matter Part 9

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Q: 23. A sample of paramagnetic salt contains atomic dipoles each of dipole moment. The sample is placed under a homogeneous magnetic field of, and cooled to a temperature of . The degree of magnetic saturation achieved is equal to . What is the total dipole moment of the sample for a magnetic field of and a temperature of ? (Assume Curie’s law)

Answer:

Number of atomic dipoles,

Dipole moment of each atomic dipole,

When the magnetic field,

The sample is cooled to a temperature,

Total dipole moment of the atomic dipole,

Magnetic saturation is achieved at.

Hence, effective dipole moment,

When the magnetic field,

Temperature,

Its total dipole moment

According to Curie’s law, we have the ratio of two magnetic dipoles as:

Therefore, is the total dipole moment of the sample for a magnetic field of and a temperature of.

Q: 24. A Rowland ring of mean radius has turns of wire wound on a ferromagnetic core of relative permeability. What is the magnetic field in the core for a magnetising current of?

Answer:

Mean radius of a Rowland ring,

Number of turns on a ferromagnetic core,

Relative permeability of the core material,

Magnetising current,

The magnetic field is given by the relation:

Where,

Permeability of free space

Therefore, the magnetic field in the core is.

Q: 25. The magnetic moment vectors and associated with the intrinsic spin angular momentum and orbital angular momentum , respectively, of an electron are predicted by quantum theory (and verified experimentally to a high accuracy) to be given by:

,

Which of these relations is in accordance with the result expected classically? Outline the derivation of the classical result.

Answer:

The magnetic moment associated with the intrinsic spin angular momentum (l) is given as

The magnetic moment associated with the orbital angular momentum (l) is given as

For current i and area of cross-section A, we have the relation:

Magnetic moment

Where,

Charge of the electron

Radius of the circular orbit

Time taken to complete one rotation around the circular orbit of radius r

Angular momentum,

Where,

Dividing equation (1) by equation (2), we get:

Therefore of the two relations, is in accordance with class physics.