Answer
$\epsilon_0~(\frac{d\phi_e}{dt})$ has units of current.
Work Step by Step
$\epsilon_0 = 8.854\times 10^{-12}~\frac{C^2}{N \cdot m^2}$
$\frac{d\phi_e}{dt}$ is the rate of change of electric flux and it is measured in units of $\frac{(N/C)~m^2}{s}$
We can find the units of $~~\epsilon_0~(\frac{d\phi_e}{dt})$:
$\frac{C^2}{N \cdot m^2}~\frac{(N/C)~m^2}{s}$
$= \frac{C}{m^2}~\frac{m^2}{s}$
$= \frac{C}{s}$
$= A$
where $A$ represents amperes, which are the units of current.
$\epsilon_0~(\frac{d\phi_e}{dt})$ has units of current.
