The magnetic susceptibility of a certain magnetic material is given...

The ratio of the magnetic permeability of the material ($\mu$) to the magnetic permeability of free space ($\mu_0$) is defined as the relative magnetic permeability ($\mu_r$).

The relationship between relative magnetic permeability and magnetic susceptibility ($\chi$) is given by:
$\mu_r = 1 + \chi$

Given that $\chi = 599$, we have:
$\mu_r = 1 + 599 = 600$

Therefore, the ratio $\dfrac{\mu}{\mu_0}$ is $600$.

Answer: $600$