Question

The relation between total magnetic field \( B \), magnetic intensity \( H \), permeability of free space \( \mu_0 \) and susceptibility \( x \) is

• A. \( \frac{B}{H} = \mu_0 (1 + x) \)
• B. \( \frac{H}{B} = \mu_0 (1 - x) \)
• C. \( \frac{B}{H} = \mu_0 (1 - x) \)
• D. \( \frac{H}{B} = \mu_0 (1 + x) \)

Hint:

In electromagnetism, the total magnetic field is influenced by both the magnetic intensity and the susceptibility of the material. The relationship \( B = \mu_0 H (1 + x) \) holds true for materials with magnetic susceptibility \( x \).

Answer 1

The Correct Option is A

Step 1: Understanding the relation.
The total magnetic field \( B \) is related to the magnetic intensity \( H \) by the equation: \[ B = \mu_0 (H + M) \] where \( M \) is the magnetization. The magnetization \( M \) is related to the magnetic susceptibility \( x \) by: \[ M = xH \] Substituting this into the equation for \( B \), we get: \[ B = \mu_0 (H + xH) = \mu_0 H (1 + x) \] Thus, the relation is: \[ \frac{B}{H} = \mu_0 (1 + x) \] Step 2: Conclusion.
Thus, the correct answer is (A) \( \frac{B}{H} = \mu_0 (1 + x) \).