Show that the quantity has units of current. ?

Question

Show that the quantity eo(d(Ie)/dt) has units of current.

Reading it as epsilon not times the change in electrc flux divided by the change in time.

Answer 1

Units for current (i):  A = C/s (amp = coulomb per second)

Units for electric flux (Φ):  (N*m²)/C

{Gauss' Law:  ÃŽÂ¦ = E * A = N/C * m² = (N*m²)/C}

Units for constant for permittivity of free space (ε₀):  C²/(N*m²)

Units for time (t):  s

Using formulas for current (i) and electric flux (Φ):

i = q/t  Ã¢Â†Â’  q = i*t

Φ = q/ε₀  Ã¢Â†Â’  q = Φ*ε₀

Set q = q:

i*t = Φ*ε₀  Ã¢Â†Â’  i = (Φ*ε₀)/t

i = (Φ*ε₀)/t = [(N*m²)/C * C²/(N*m²)] / s = [(N*m²*C²) / (C*N*m²)] / s = C/s = A