Question

A capacitor consists of two square plates, 8.7 cm on a side, separated by a 2.0 mm air gap. How much energy would be stored in the capacitor if a mica dielectric is placed between the plates? Assume the mica is 2.0 mm thick (and therefore fills the space between the plates).The charges on the plates are equal and opposite and of magnitude 240 μC .

Answer 1

122.84 J

Step-by-step explanation:

Since plate is square, area, A is given by
`(8.7/100)^(2)=0.007569m^(2)`

The distance between plates, d, is given in the question as 2mm=0.002m

Charge on plate, Q, as given in the question is 240
`\mu c`

Assuming mica dielectric constant, k of 7

Capacitance, C is given by

C=
`\frac {k\epsilon_(o)A}{d}=\frac {(7)(8.85*10^(-12))(0.007569)}{0.002}=2.34*10*^(-10)F`

Stored energy, E is given by

E=
`\frac {Q^(2)}{2C}=\frac {(240*10^(-6))^(2)}{2*(2.34*10^(-10))}=122.84J`

Therefore, the stored energy is 122.84 J