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

Question

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

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Answer 1 · 2017-04-26T18:09:39

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:

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