How to check units? I've got: $Q=\frac{Er^2}{k}$
how to check the units?
I start with $\left[\frac{\text V}{\text m} \,  \text m^2\right]$, tried replacing $[ \text V ]$ with $\left[ \frac{\text J}{\text C} \right]$, but it's not leading me to $[\text C]$.
 A: First of all note that $k$ is not dimensionless, it is $k = \frac{1}{4 \pi \varepsilon_0}$, and $\varepsilon_0$ has dimensions of $\frac{ \text C^2}{ \text {N m}^2}$. So you have already $\frac{ \text{V C}^2 \text m^2}{ \text {N m m} ^2}$. Also, volt can be expanded as $ \text V = \frac{ \text {N m}}{ \text C}$, so one gets
$$ \frac{ \text C^2}{ \text {N m}^2} = \frac{ \text{V C}^2\text { m}^2}{ \text {N m m}^2} = \frac{ \text C^2}{ \text {N m}} \frac{ \text {N m}}{ \text C} = \text C$$
- exactly what you were looking for.
A: When in doubt, break everything down into a set of indivisible units: kilograms, meters, seconds, and coulombs.  So ask yourself what is a joule in terms of those units, and also consider that the constant $k$ has units.  You can figure out what those units are by writing out Coulomb's law.
Edit: the units of $\epsilon_0$ can be found as follows.  You know Coulomb's law.
$$E = \frac{1}{4\pi \epsilon_0} \frac{q}{r^2}$$
Rearrange this to solve for $\epsilon_0$:
$$\epsilon_0 = \frac{1}{4\pi E} \frac{q}{r^2}$$
You know that $E$ is measured as force per unit charge.  The other quantities are charges and lengths (or dimensionless constants).  The result is
$$\epsilon_0 = \frac{\text{[charge]}^2}{\text{[force]} \times \text{[length]}^2}$$
