Question

Two parallel plates that are initially uncharged are separated by 1.2 mm. What charge must be transferred from one plate to the other if 11.0 KJ of energy are to be stored in the plates, if area of each plate is 19.0 mm

Answer 1

Answer:

$Q=55.5 \mu C$

Explanation:

We start by writing the formula of the energy stored between two charged parallel plates, which is:

$U=\frac{Q^2}{2C}$

Where Q is the charge on one of the plates and C its capacitance, which for two parallel plates is:

$C=\frac{\epsilon A}{d}$

Where A is the area of each plate, d the distance between them and $\epsilon$ the permittivity of the medium, in our case the vacuum, $\epsilon_0$.

Putting all together:

$U=\frac{Q^2d}{2\epsilon_0 A}$

Which means:

$Q=\sqrt{\frac{U2\epsilon_0 A}{d}}$

Which for our values is:

$Q=\sqrt{\frac{(11\times10^3J)2(8.85\times10^{-12}F/m)(0.000019m^2)}{(0.0012m)}}=55.5\times10^{-6}C$