Question

An electric field of 8.30 x 10^5 V/m is desired between two parallel plates, each of area 31.5 cm^2 and separated by 2.45 mm. There's no dielectric. What charge must be on each plate?

Answer 1

Charge on each plate = 2.31 x 10⁻⁸ C

Step-by-step explanation:

We have the equations

`E=(V)/(d)\texttt{ and }V=(Q)/(C)`

Combining both equations

`E=(\left ((Q)/(C)\right ))/(d)=(Q)/(Cd)`

We also have the equation for capacitance

`C=(\epsilon A)/(d)`

That is

`E=(Q)/((\epsilon A)/(d)* d)=(Q)/(\epsilon A)\\\\Q=\epsilon AE`

Substituting

`Q=8.85* 10^(-12)* 31.5* 10^(-4)* 8.30* 10^5=2.31* 10^(-8)C`

Charge on each plate = 2.31 x 10⁻⁸ C