Electrostatic Potential and Capacitance

A parallel-plate capacitor of capacitance 40 is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant K=2. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are

1. 8 mC and 2.0 J
2. 4 mC and 0.2 J
3. 2 mC and 0.2 J
4. 2 mC and 0.4 J

Answer

(2) 4 mC and 0.2 J

Solution

The battery stays connected: V=100 V; C'=KC=80 F.

Q=(C'-C)V=40 10-6 100=4 mC

U= 12(C'-C)V2= 12 40 10-6 104=0.2 J

Answer: (2)