Question

The relationship between the magnetic susceptibility (\(\chi\)) and magnetic permeability (\(\mu\)) of a material is (\(\mu _{0}\) and \(\mu _{r}\) is the permeability of free space and relative permeability respectively)

• A. \(\chi =\frac{\mu }{\mu _{0}}-1\)
• B. \(\chi =\frac{\mu _{r}}{\mu _{0}}+1\)
• C. \(\chi =\mu _{r}+1\)
• D. \(\chi =1-\frac{\mu }{\mu _{0}}\)

Hint:

Start from the relative permeability equal to 1 plus the susceptibility.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Relative permeability and susceptibility are related by \(\mu_r=1+\chi\).

Step 2: Use permeability
\(\mu_r=\dfrac{\mu}{\mu_0}\).

Step 3: Combine
\(\chi=\mu_r-1=\dfrac{\mu}{\mu_0}-1\).

Step 4: Compare the options
This is option (A).

Final Answer:
The susceptibility equals mu over mu naught minus 1. \[ \boxed{\text{(A) }\chi=\dfrac{\mu}{\mu_{0}}-1} \]