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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) $\mathrm{B}=\mu_{0}(\mathrm{H}+\mathrm{M})$

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.

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.