Question

3. Energy of a capacitor. [20] A parallel-plate capacitor has area A and plate separation d. Initially the capacitor has an air gap (K=1). (a) The capacitor is connected to a battery with voltage (EMF) E. What is the strength of the clectric field inside the capacitor? (5) (b) What is the charge on the capacitor? [5] The capacitor is disconnected from the battery. Then a metal block (K=0 ) with the same area and thickness d/2 is inserted into the gap, leaving two gaps that are d/4 wide. (c) What is the voltage on the capacitor afterwards? [5] (d) What is the change of energy of the capacitor during this process? [5]

Answer 1

3.

a)

$\Delta$V = potential difference across the plates of capacitor = $\varepsilon$

d = plate separation

E = electric field between the plates

Electric field between the plates is given as

E = $\Delta$ V/d

E = $\varepsilon$ /d

b)

A = Area of each plate

Capacitance of the capacitor is given as

C = $\epsilon _{o}$ A/d

$\Delta$V = potential difference across the plates of capacitor = $\varepsilon$

Q = charge stored by capacitor

Charge on the capacitor is given as

Q = C $\Delta$ V

Q = ($\epsilon _{o}$A/d) $\varepsilon$

Q = $\epsilon _{o}$ $\varepsilon$A/d