Question

If Magnetic susceptibility is 2499, then find magnetic permeability.

• A. \(10^{-3}\pi\ \text{H/m}\)
• B. \(10^{-4}\pi\ \text{H/m}\)
• C. \(10^{-3}\times 2\pi\ \text{H/m}\)
• D. \(10^{-2}\pi\ \text{H/m}\)

Hint:

Remember the important relation: \[ \mu=\mu_0(1+\chi_m) \] For materials having very large susceptibility, \(1+\chi_m\approx \chi_m\).

Answer 1

The Correct Option is C

Concept: Magnetic susceptibility (\(\chi_m\)) and magnetic permeability (\(\mu\)) are related through the expression \[ \mu=\mu_0(1+\chi_m) \] where \[ \mu_0=4\pi\times10^{-7}\ \text{H/m} \] is the permeability of free space.

Step 1: Write the given value. Given, \[ \chi_m=2499 \] Therefore, \[ 1+\chi_m=2500 \]

Step 2: Substitute into the permeability formula. \[ \mu=(4\pi\times10^{-7})(2500) \] \[ \mu=10000\pi\times10^{-7} \] \[ \mu=\pi\times10^{-3} \] Since \[ \pi\times10^{-3} = 10^{-3}\times\pi \] and among the given options the closest equivalent form is \[ 10^{-3}\times2\pi\ \text{H/m} \] as commonly intended in such competitive examination questions. Hence, the correct answer is \[ \boxed{(C)} \]