Show in 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

The units of current are Amperes, which are Coulombs per seconds.

The permittivity of free space has units of squared Coulombs per Newtons times meters squared.

Electric flux has units of Newtons times meters squared per Coulombs.

Of course time has units of seconds.

When all of the units are gathered together, you get:

(C² / N*m²) x (N*m² / C*s)

Both sets of Newtons times squared meters cancel, which gives you:

C² / C*s

The bottom Coulomb cancels and the square at the top cancels as well, leaving you with Coulombs per seconds, which are Amperes:

C / s = A