# Physics Class 12 NCERT Solutions: Chapter 5 Magnetism and Matter Part 9 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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.