Question

Assertion:
Magnetic susceptibility is a pure number.
Reason:
The magnetic susceptibility for vacuum is one.
(A). Both assertion and reason are correct and reason is the correct explanation for assertion
(B). Both assertion and reason are correct but reason is not the correct explanation for assertion
(C). Assertion is correct but reason is incorrect
(D). Both assertion and reason are incorrect

Answer 1

Hint: Assertion is a statement and reasoning may or may not be its explanation. Here magnetic susceptibility is the ratio of magnetization to applied magnetic field; its value is different for different magnetic materials. It depends on the nature of magnetic material and the strength of the applied field.

Complete solution:
The magnetic susceptibility describes how much a material will get magnetized when kept in a magnetic field. The magnetic susceptibility is the ratio of magnetization to the applied magnetic field. It is given by-
$\chi =\dfrac{M}{H}$
Here,
$\chi $ is the magnetic susceptibility
$M$ is the magnetization of the material
$H$is the applied magnetic field.

It is negative for those materials that show diamagnetism and positive for materials that show paramagnetism. Also its value is greater than one for ferromagnetic materials.
Since susceptibility is a ratio, it does not have any unit and is a pure number.
The susceptibility of vacuum is 0 as vacuum cannot be magnetized.

Therefore, as susceptibility is a ratio, it is a pure number but the susceptibility of vacuum is not one but zero.

Hence, the correct option is (C).

Additional Information:
Permeability is a property of a medium, it is the measure of ability of a medium to develop a magnetic field inside it when kept in an external magnetic field. The permeability of free space or vacuum is known as the vacuum permeability and is denoted by ${{\mu }_{0}}$.

Note:
Magnetization is defined as the magnetic moment per unit volume. Magnetic moment is the product of pole strength and the distance between the poles. When the direction of magnetic moments in a material is opposite to the applied magnetic field, then the material is said to be paramagnetic, when the direction of magnetic moments is the same as the direction of applied magnetic field then the material is said to be diamagnetic.