Peoples Physics Book Version-3

12.6. Electric Field of a Parallel Plate Capacitor http://www.ck12.org

12.6 Electric Field of a Parallel Plate Capacitor

Suppose we have two parallel metal plates set a distancedfrom one another. We place a positive charge on one of
the plates and a negative charge on the other. In this configuration, there will be a uniform electric field between the
plates pointing from, and normal to, the plate carrying the positive charge. The magnitude of this field is given by

E=

V

d

whereVis the potential difference (voltage) between the two plates.

The amount of charge,Q, held by each plate is given by

Q=CV

where againVis the voltage difference between the plates andCis the capacitance of the plate configuration.
Capacitance can be thought of as the capacity a device has for storing charge. In the parallel plate case the
capacitance is given by

C=

ε 0 A

d

whereAis the area of the plates,dis the distance between the plates, andε 0 is the permittivity of free space whose
value is 8. 84 × 10 −^12 C/V·m.

The electric field between the capacitor plates stores energy. The electric potential energy,UC, stored in the capacitor
is given by

UC=

1

2

CV^2

Where does this energy come from? Recall, that in our preliminary discussion of electric forces we assert that “like
charges repel one another”. To build our initial configuration we had to place an excess of positive and negative
charges, respectively, on each of the metal plates. Forcing these charges together on the plate had to overcome the
mutual repulsion that the charges experience; this takes work. The energy used in moving the charges onto the plates
gets stored in the field between the plates. It is in this way that the capacitor can be thought of as an energy storage
device. This property will become more important when we study capacitors in the context of electric circuits in the
next chapter.

Note: Many home-electronic circuits include capacitors; for this reason, it can be dangerous to mess around with old
electronic components, as the capacitors may be charged even if the unit is unplugged. For example, old computer
monitors (not flat screens) and TVs have capacitors that hold dangerous amounts of charge hours after the power is
turned off.