The magnetic susceptibility of the material of a rod is 499. Permeability of vacuum is \( 4\pi \times 10^{-7}\,\mathrm{H/m} \). The absolute permeability of the material of the rod is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 2\pi \times 10^{-4}\,\mathrm{H/m} \)
The relative permeability is related to the magnetic susceptibility by \( \mu_r = 1 + \chi \), and the absolute permeability is \( \mu = \mu_0\mu_r \).
\( \displaystyle \mu_r = 1 + \chi = 1 + 499 = 500 \)
\( \displaystyle \mu = \mu_0\mu_r = 4\pi\times10^{-7}\,\mathrm{H/m} \times 500 = 2000\pi\times10^{-7}\,\mathrm{H/m} \)
\( \displaystyle \mu = 2\pi\times10^{-4}\,\mathrm{H/m} \)