The magnetic susceptibility of the material of a rod is 499. Permeability of vacuum is $4\pi × 10^{-7} H/m$. The absolute permeability of the material of the rod is

$2π × 10^{-4} H/m$

The correct answer is Option (3) → $2π × 10^{-4} H/m$

Given:

Magnetic susceptibility, $\chi_m = 499$

Permeability of vacuum, $\mu_0 = 4\pi \times 10^{-7}\ \text{H/m}$

Absolute permeability of the material:

$\mu = \mu_0 (1 + \chi_m)$

Substitute values:

$\mu = 4\pi \times 10^{-7} (1 + 499) = 4\pi \times 10^{-7} \cdot 500 = 2 \times 10^{-4} \pi\ \text{H/m}$

∴ Absolute permeability of the material = $2 \pi \times 10^{-4}\ \text{H/m}$