Question

A parallel-plate air capacitor of area A= 14.0 cm² and plate separation d= 2.20 mm is charged by a battery to a voltage 56.0 V. If a dielectric material with κ = 4.00 is inserted so that it fills the volume between the plates (with the capacitor still connected to the battery), how much additional charge will flow from the battery onto the positive plate?

Answer 1

here,

Area = 14 cm^2 = 14 * 10^-4 m^2

sepration , d = 2.2 mm = 2.2 * 10^-3 m

potential difference , V = 56 V

dielectric constant , k = 4

the initial charge , Q1 = area * e0 /d * V

final charge , Q2 = area * e0 * k /d * V

so, the additional charge will flow from the battery onto the positive plate , Q = Q2 - Q1

Q = area * e0 * V /d * ( k - 1)

Q = 14 * 10^-4 * 8.85 * 10^-12 * 56 /( 2.2 * 10^-3) * ( 4 - 1)

Q = 9.46 * 10^-10 C

the additional charge will flow from the battery onto the positive plate is 9.46 * 10^-10 C