Confirming the dimension of induced charge density of a dielectric

[patric44]

Homework Statement

confirm the dimension of induced charge density of a dielectric ρ and σ

Relevant Equations

ρ = -1/4πk E.grad(k)

hi guys
our professor asked us to confirm the units of volume charge density ρ and also the surface charge density σ of a dielectric material given by
$$
\rho = \frac{-1}{4\pi k} \vec{E}\cdot\;grad(k)
$$
$$
\sigma= \frac{-(k-1)}{4\pi} \vec{E_{1}}\cdot\;\vec{n}
$$
I am somehow confused about the units, shouldn't the gradiant of k (the dielectric constant ) be dimensionless.
but that will leave ρ as the same units of E, which is not true as ρ =C/m^3.
can someone clarify

 

[TSny]

$k$ is dimensionless, but grad($k$) is not.

Is your professor using Gaussian units?

 

[patric44]

thanks, by careful looking at the gradient operator i can see that it has a unit of 1/length