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For an isotropic medium B, $\mu $, H and M are related as (where B, ${{\mu }_{0}}$,H) and M have their usual meaning in the context of magnetic material:
A) $(\mathrm{B}-\mathrm{M})=\mu_{0} \mathrm{H}$
B) $\mathrm{M}=\mu_{0}(\mathrm{H}+\mathrm{M})$
C) $\mathrm{H}=\mu_{0}(\mathrm{H}+\mathrm{M})$
D) $\mathrm{B}=\mu_{0}(\mathrm{H}+\mathrm{M})$

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Last updated date: 22nd Feb 2024
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Hint: We should know by an isotropic medium we mean that the medium will be uniform in all the directions. The simplest of this kind of a medium is known as a space. To answer we need to consider the expression to find the magnetic induction involving the homogenous magnetic field.

Complete step by step answer:
We know that by the term magnetic induction we mean the induction that is developed because of magnetism inside a body when the body is placed in a magnetic field. The induction is produced even when the body experiences the development of flux through it because of the presence of some magnetomotive force.
The expression for the net magnetic induction is given as: $\mathrm{B}=\mathrm{B}_{0}+\mathrm{NB}_{\mathrm{m}}$
In the above expression,
B is the magnetic induction, N is the number of turns, ${{B}_{0}}$ is the homogeneous magnetic field and then ${{B}_{m}}$ is the magnetic field.
The expression can be written as: $\mu_{0} \mathrm{H}+\mu_{0} \mathrm{M}$
Here M stands for magnetization and H is defined as the vector quantity which has both the direction and the magnitude and is known as magnetic field intensity.
So, we can write the final expression as: $\mathrm{B}=\mu_{0}(\mathrm{H}+\mathrm{M})$

Hence the correct answer is Option D.

Additional Information:
The instrument that is used to measure the magnetic field strength is known as magnetometer. The magnetic field strength is also defined in terms of units of Gauss.

Note: We should know that the magnetic field intensity is defined as the magnetic field that develops because of the effect of the external current and is not an inbuilt property of material. The unit is which the magnetic field intensity is measured in amperes per metre. The SI unit is known as Tesla.