Question

A metal rod of susceptibility \(799\) is subjected to a magnetising field of \(2000\,\text{A m}^{-1}\). The permeability of the material of the rod is: (Given \(\mu_0 = 4\pi \times 10^{-7}\,\text{T m A}^{-1}\))

• A. \(4.2\pi \times 10^{-7}\,\text{T m A}^{-1}\)
• B. \(3.2\pi \times 10^{-4}\,\text{T m A}^{-1}\)
• C. \(2.4\pi \times 10^{-5}\,\text{T m A}^{-1}\)
• D. \(80\pi \times 10^{-7}\,\text{T m A}^{-1}\)

Hint:

Permeability depends on susceptibility using \(\mu = \mu_0(1+\chi)\). Field strength is not needed unless magnetisation is asked.

Answer 1

The Correct Option is B

Step 1: Use relation between permeability and susceptibility.
The permeability of a material is given by:
\[ \mu = \mu_0 (1 + \chi) \]
where \(\chi\) is magnetic susceptibility.

Step 2: Substitute given values.
\[ \chi = 799 \]
\[ \mu_0 = 4\pi \times 10^{-7} \]

Step 3: Calculate \(1 + \chi\).
\[ 1 + \chi = 1 + 799 = 800 \]

Step 4: Substitute into formula.
\[ \mu = 4\pi \times 10^{-7} \times 800 \]

Step 5: Simplify the expression.
\[ \mu = 3200\pi \times 10^{-7} \]
\[ \mu = 3.2\pi \times 10^{-4} \]

Step 6: Final answer.
\[ \boxed{3.2\pi \times 10^{-4}\,\text{T m A}^{-1}} \]

Step 7: Note about field value.
The given magnetising field \(2000\,\text{A m}^{-1}\) is not required in this calculation since permeability depends only on \(\mu_0\) and \(\chi\).