Introductory Physics Volume Two

2.4 Capacitors 45
§ 2.4 Capacitors
Suppose that we place two conductors near each other. Now suppose
that we remove a quantity of charge Q from one conductor and
place it on the other. One conductor will end up with a charge +Q and
the other will end up with a charge −Q. In addition an electric field
will be created between the conductors.
Since there is an electric field between the conductors, there will also
be an electric potential difference between the two conductors.
∆V = V + − V − = −
∫ ⃗r+
⃗r −
⃗ E · ⃗ dr
Because the electric field strength is proportional to the charge Q, the
electric potential difference will also be proportional to Q.
∆V ∝ Q
Example
Here is a specific example of this general result. Place two conducting
plates parallel to each other as shown, and charge the top plate to a
net charge Q and the other plate to a net charge −Q
In a previous example it was shown that the electric field strength near
a plate with uniform charge density σ is E = σ/2ɛ 0 . Between the
plates the fields of the two plates are in the same direction (toward
the negatively charged plate) so that the strength of the net field is
twice the field strength of each plate alone. So the net field between
the plates is E = σ/ɛ 0 . If the area of the plate is A then the charge