An iron rod of susceptibility $599$ is subjected to a magnetizing field of $1200 ext{ A m}^{-1}$. The permea

Question

An iron rod of susceptibility $599$ is subjected to a magnetizing field of $1200 	ext{ A m}^{-1}$. The permeability of the material of the rod is: $(\mu_0 = 4\pi 	imes 10^{-7} 	ext{ T m A}^{-1})$

Accepted Answer

1. **Concept:** The magnetic permeability ($\mu$) of a material is related to its magnetic susceptibility ($\chi$) and the permeability of free space ($\mu_0$).
2. **Formula:** 
   The relative permeability is given by $\mu_r = 1 + \chi$.
   The absolute permeability is given by $\mu = \mu_0 \mu_r = \mu_0 (1 + \chi)$.
3. **Given Data:**
   - Susceptibility, $\chi = 599$.
   - Permeability of free space, $\mu_0 = 4\pi 	imes 10^{-7} 	ext{ T m A}^{-1}$.
   - Magnetizing field $H = 1200 	ext{ A m}^{-1}$ (This data is extra and not required to find permeability).
4. **Calculation:**
   $$ \mu_r = 1 + 599 = 600 $$
   $$ \mu = 4\pi 	imes 10^{-7} 	imes 600 $$
   $$ \mu = 2400\pi 	imes 10^{-7} $$
   $$ \mu = 2.4\pi 	imes 10^{-4} 	ext{ T m A}^{-1} $$

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