Question

The relationship between the magnetic susceptibility $ \chi $ and the magnetic permeability $ \mu $ is given by: 
$ \mu_0 $ is the permeability of free space and $ \mu_r $ is relative permeability.

• A. \( \chi = \frac{\mu}{\mu_0} - 1 \)
• B. \( \chi = \frac{\mu + 1}{\mu_0} \)
• C. \( \chi = \mu_r + 1 \)
• D. \( \chi = 1 - \frac{\mu}{\mu_0} \)

Hint:

In problems involving magnetic susceptibility, remember that the relative permeability \( \mu_r \) is directly related to \( \chi \), and permeability \( \mu \) is proportional to \( \mu_0 \times \mu_r \).

Answer 1

The Correct Option is A

We have: \[ \mu_r = (1 + \chi) \quad \text{so} \quad \chi = (\mu_r - 1) \] Also, \[ \mu = \mu_0 \mu_r \quad \Rightarrow \quad \mu_r = \frac{\mu}{\mu_0} \] Thus, \[ \chi = \frac{\mu}{\mu_0} - 1 \]