Question

The relation between B, H and I in S.I units is:
$\begin{align}
  & \text{A}\text{. }B={{\mu }_{0}}\left( H+I \right) \\
 & \text{B}\text{. }B=H+4\pi I \\
 & \text{C}\text{. }H={{\mu }_{0}}\left( B+I \right) \\
 & \text{D}\text{. None of these}\text{.} \\
\end{align}$

Answer 1

Hint: We know that magnetic intensity denoted by H is a quantity which describes magnetic phenomenon in terms of their magnetic fields. The strength of the magnetic field at a point can be given in terms of H. The intensity of magnetization is responsible for the magnetic field and the magnetic intensity along with the permeability of vacuum.

Complete step by step answer:
A quantity known as magnetic intensity is used in describing magnetic phenomenon in terms of magnetic field.
Magnetic intensity ‘H’ is given by the relation $B={{\mu }_{0}}H..........\left( 1 \right)$
Where, H represents the magnetic intensity
B represents the magnetic field.
Magnetic field can be written as –
$B={{\mu }_{0}}\left( H+{{M}_{Z}} \right)........\left( 2 \right)$
Where, ${{M}_{Z}}=\text{Magnetization}$
Magnetization & magnetic intensity is mathematically expressed as –
${{M}_{Z}}=XH..........\left( 3 \right)$
Where, X= Magnetic susceptibility.
As we know that magnetic susceptibility is small and positive for paramagnetic materials whereas magnetic susceptibility is small and negative for diamagnetic materials.
From equation (1), (2) & (3), we can write it as –
$B={{\mu }_{0}}\left( 1+X \right)H$
Therefore, $B={{\mu }_{0}}{{\mu }_{r}}H$
$\therefore B=\mu H\left( \because \mu ={{\mu }_{0}}{{\mu }_{r}} \right)$
Where, ${{\mu }_{r}}=1+X$
${{\mu }_{r}}$ is known as the relative magnetic permeability of the substance and this quantity is a dimensionless quantity.
Let I be the intensity of the magnetization & B is magnetic field inside the substance then magnetic intensity H in vector from can be written as –
$H=\dfrac{B}{{{\mu }_{0}}}-I$
Further solving
$\begin{align}
  & {{\mu }_{0}}H=B-I{{\mu }_{0}} \\
 & {{\mu }_{0}}H+{{\mu }_{0}}I=B \\
 & {{\mu }_{0}}\left( H+I \right)=B \\
 & B={{\mu }_{0}}\left( H+I \right) \\
\end{align}$
The relation between B, H and I is $B={{\varpi }_{0}}\left( H+I \right)$ . Therefore, Option (A) is the correct answer.

Note:
Above expression is applicable or valid for substances or presence of material. In the absence of any material, the value of intensity of magnetization is zero. Then magnetic intensity is written as –
$H=\dfrac{B}{{{\mu }_{0}}}$ .