What is the dimensional analysis for N/C to V/m?

Question

I know that they are equal and I have a basic grasp of the units involved, but I can't figure out how to make the jump from point A to point B.

Answer 1

The root SI units here are kg, m, s and A.

N = (kg m) / (s²)

C = A s

V = (kg m²) / (A s³)

I had to back-derive V, though...it's rarely expanded out into core SI units.  :)

m = m

So, N/C = (kg m) / ((s²)(A s) = (kg m) / (A s³)

V/m = (kg m²) / (A s³ m) = (kg m) / (A s³)