Question

If $M$ is the magnetisation induced in the material, H is the magnetic field intensity, B is the net magnetic field inside the material then the correct relation between them is ( $\mu_0 = \text{permeability of free space}$)

• A. $\text{B} = \frac{\mu_0}{(\text{H+M})}$
• B. $B = \mu_0(H - M)$
• C. $\text{B} = \frac{\mu_0}{(\text{H-M})}$
• D. $B = \mu_0(H + M)$

Hint:

Total field = (Field in vacuum) + (Field due to medium).

Answer 1

The Correct Option is D

Step 1: Concept
The total magnetic field $B$ in a material is the sum of the magnetic field due to external current ($B_0 = \mu_0 H$) and the magnetic field due to the material's magnetization ($B_m = \mu_0 M$).

Step 2: Meaning
$B$ represents magnetic induction, $H$ is the magnetic intensity (external), and $M$ is the intensity of magnetization (internal response).

Step 3: Analysis
Mathematically, $B = B_0 + B_m = \mu_0 H + \mu_0 M$. Factoring out $\mu_0$ gives $B = \mu_0(H + M)$.

Step 4: Conclusion
The correct vector relation is $B = \mu_0(H + M)$. Final Answer: (D)