### Equipotential Lines - Tenafly Public Schools

```-Capacitors and Capacitance
AP Physics C
Mrs. Coyle
Capacitors: devices that store electric
charge

Consist of two isolated conductors (plates)
with equal and opposite charges +Q and −Q;
the charge on the capacitor is referred to as
"Q".
Ex:Parallel Plate
Capacitor
Applications of Capacitors



Used as filters in power supplies
Used as energy-storing devices in electronic
flashes (ex: cameras)
Charging a Parallel Plate Capacitor





The battery establishes a field on the
plates.
This forces the electrons from the wire
to move on to the plate that will become
the negative plate.
This continues until equilibrium is
achieved(the plate, the wire and the terminal
are all at the same potential) and the
movement of the electrons ceases.
At the other plate, electrons move away
from the plate, leaving it positively
charged.
Finally, the potential difference across
the capacitor plates is the same as that
between the terminals of the battery.
Capacitor Animation

or-lab
Capacitance: a measure of the
capacitor’s ability to store charge
Q
C
V




Ratio of the magnitude of the charge on either
conductor to the potential difference between the
conductors.
The SI unit of capacitance is the farad (F)
1 F = 1 Coulomb/Volt
Also see the units pF (10-12) or mF (10-6)
Factors that affect capacitance


Size (Area, distance between
plates)
Geometric arrangement




Plates
Cylinders
Spheres
Material between plates
(dielectric)



Air
Paper
Wax
Note:

Capacitance is always positive

The capacitance of a given capacitor is
constant. If the voltage changes the charge
will change not the capacitance.
Note:

The electric field is uniform in the central region, but not at
the ends of the plates. It is zero elsewhere.

If the separation between the plates is small compared
with the length of the plates, the effect of the non-uniform
field can be ignored.
Capacitance
of a Parallel
Plate
Capacitor



Q
Q
C

V Ed
From Gauss's Law EA=Q/εo
Q
C
Qd / εo A
εo A
C
d
A is the area of each plate
Q is the charge on each plate, equal with opposite signs
The capacitance is proportional to the area
of its plates and inversely proportional to the
distance between the plates
A single conductor can have a
capacitance.

Example: Isolated charged sphere can be
thought of being surrounded by a concentric
shell of infinite radius carrying a charge of the
same magnitude but opposite sign.
Capacitance of an Isolated Charged
Q
Sphere, Cont’d
C 
V
V  k eQ / R

Assume V = 0 at infinity

Note, the capacitance
is independent of the
charge and the
potential difference.
Q
C 
k eQ / R
R
C
 4πεo R
ke
Capacitance of a
Cylindrical Capacitor

From Gauss’s Law, the
field between the
cylinders is
E = 2ke l/ r, lQ/L
b
 Q 
Q
dr
Q
b
Vba    

ln  
  dr   

2o rL 
2o L a r
2o L  a 
a
b

V = -2ke l ln (b/a)
Q
C

V 2ke ln  b / a 
Capacitance of a Spherical Capacitor

Potential difference:
 1 1
V  keQ   
b a

Capacitance:
Q
ab
C

V ke  b  a 
```