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: Understanding the Concept:
When a material is subjected to an external magnetic field, it develops its own magnetization.
The total magnetic field (magnetic induction $B$) inside the material is the superposition of the applied field and the field originating from the material's magnetization.
Step 2: Key Formula or Approach:
Applied external field $B_0 = \mu_0 H$.
Induced field due to material $B_M = \mu_0 M$.
Net field $B = B_0 + B_M$.
Step 3: Detailed Explanation:
The total magnetic field $B$ is the vector sum of the contribution from external free currents (represented by $H$) and the contribution from the material's bound currents (represented by magnetization $M$).
\[ B = \mu_0 H + \mu_0 M \] Factoring out the permeability of free space $\mu_0$: \[ B = \mu_0(H + M) \] This is the standard defining relation in magnetostatics in matter.
Comparing with the given options, option D matches exactly.
Step 4: Final Answer:
The correct relation is $B = \mu_0(H + M)$.