Question

What is the electric field strength, the energy stored and the electric flux density of ?

A capacitor consisting of two metal plates each of an area of 50cm^2 and spaced 0.2mm apart in air and also connected across a 120V supply

Answer 1

The electric field inside a parallel plate is uniform. The calculation follows from a more general relationship:

`E = (Delta V(x))/(Delta x)`

Instead of defining terms, I'll just plug them in so you can see for yourself. So here:

`E = 120/(0.2 cdot 10^(-3)) = 0.6 cdot 10^6 \ "V/m"`

One expression for the potential energy stored in the capacitor is:

`U = 1/2 CV^2`

We need the capacitance :

`C = (varepsilon_r varepsilon_o A)/d`, because the gap is air we use `varepsilon_r = 1`

`implies C = (8.85 cdot 10^(-12) times 0.005)/(0.2 cdot 10^(-3)) = 2.2 cdot 10^(-10) \ F`

`implies U = 1/2 times 2.2 cdot 10^(-10) times 120^2 approx 1.6 cdot 10^(-6) \ J`

In terms of electric flux density , `D`, one expression is:

`D = varepsilon_r varepsilon_o E = varepsilon_o E = 8.85 cdot 10^(-12) times 0.6 cdot 10^6 \ " C/"m^2`