Question

A parallel-plate air-filled capacitor having area 58 cm² and plate spacing 0.89 mm is charged to a potential difference of 520 V. Find (a) the capacitance, (b) the magnitude of the charge on each plate, (c) the stored energy, (d) the electric field between the plates, (e) the energy density between the plates.

Answer 1

here,

area of each plate , A = 58 * 10^-4 m^2

plate spacing , d = 0.89 mm = 8.9 * 10^-4 m

potential difference ,V = 520 V

a)

the capacitance , C = area * e0 /d

C= 58 * 10^-4 * 8.85 * 10^-12 /( 8.9 * 10^-4) F

C = 5.78 * 10^-11 F

b)

the magnitude of the charge on each plate , Q = C * V

Q = 5.78 * 10^-11 * 520 C

Q = 3 * 10^-8 C

c)

the energy stored , TE = 0.5 * C * V^2

TE = 0.5 * 5.78 * 10^-11 * 520^2 J

TE = 7.81 * 10^-6 N/C

d)

the electric feild between the plates , E = V/d

E = 5.8 * 10^5 N/C

e)

the energy density , U = 0.5 * e0 * E^2

U = 0.5 * 8.85 * 10^-12 * ( 5.8 * 10^5)^2

U = 1.49 J/m^3