Question

A solenoid having \(250\) turns per metre has a core of a material with relative permeability \(500\). What is the approximate value of the magnetisation of the core material, if a current of \(2\,\text{A}\) is passed through it?

• A. \(2 \times 10^{5}\ \text{A m}^{-1}\)
• B. \(1.5 \times 10^{5}\ \text{A m}^{-1}\)
• C. \(2.5 \times 10^{5}\ \text{A m}^{-1}\)
• D. \(1 \times 10^{5}\ \text{A m}^{-1}\)

Hint:

For magnetic materials with large relative permeability, magnetisation can be approximated using \(M \approx (\mu_r - 1)H\).

Answer 1

The Correct Option is C

Step 1: Magnetic field intensity inside the solenoid.
The magnetic field intensity is given by:
\[ H = nI \] \[ H = 250 \times 2 = 500\ \text{A m}^{-1} \]
Step 2: Relation between magnetisation and magnetic field.
Magnetisation \(M\) is related to magnetic susceptibility \(\chi_m\) by:
\[ M = \chi_m H \] where
\[ \chi_m = \mu_r - 1 \]
Step 3: Substitute the given values.
\[ \chi_m = 500 - 1 \approx 500 \] \[ M = 500 \times 500 = 2.5 \times 10^{5}\ \text{A m}^{-1} \]
Step 4: Conclusion.
The approximate value of magnetisation of the core material is \(2.5 \times 10^{5}\ \text{A m}^{-1}\).