We define the electric field as the force per charge. The units for this definition are newtons per coulomb. When we worked through the unit on electric potential, we related the field to the potential through the equation E = - ΔV / d. This gives the electric field units of volts per meter. Show that these two units are the same

Answer: N/C = (Kg*m) / (s^2*C)

V/m = (Kg*m) / (s^2*C)

Explanation: In order justify that N/C has the same units that V/m, we have to detail every of these units:

Then,

Newton=mass*acceleration=Kg*m/s^2 then E=N/C=Kg*m/s^2/C

On the other hand,

Voltage = Energy/charge = Joule/C = N*m/C=N*m/C=Kg * (m/s^2) * m/C,

then, E=V/m = N*m/C=[Kg * (m/s^2) ]*m / (C) * m=[Kg * (m/s^2) ]/C=N/C

Therefore

N/C has the same units that V/m