1. Use the standard relation between $\mathbf{B}$ and $\mathbf{H}$

   For a magnetic material, $B=\mu H$ and also, $B=\mu_0(1+\chi)H$

   where:

   • $\mu$ = magnetic permeability of the material
   • $\mu_0$ = permeability of free space
   • $\chi$ = magnetic susceptibility

2. Compare the two expressions

   Since both represent $B$, $\mu H=\mu_0(1+\chi)H$

   Cancelling $H$, $\mu=\mu_0(1+\chi)$

3. Solve for susceptibility

   $1+\chi=\frac{\mu}{\mu_0}$ $\chi=\frac{\mu}{\mu_0}-1$

4. Using relative permeability

   Since $\mu_r=\frac{\mu}{\mu_0}$ we can also write $\chi=\mu_r-1$

5. Check options

   • A: $X=\dfrac{\mu}{\mu_0}-1$ ✅ Correct
   • B: $X=\dfrac{\mu_r}{\mu_0}+1$ ❌ Incorrect; dimensions and relation are wrong
   • C: $\chi=\mu_r+1$ ❌ Incorrect; correct relation is $\chi=\mu_r-1$
   • D: $X=1-\dfrac{\mu}{\mu_0}$ ❌ Incorrect sign

Therefore, the correct option is A.