Chapter 20 Electric Potential and Electric Potential Energy
Section 20-1
electrical U
. This divides out the
charge
effect of the charge q0 and leaves a quantity that measures the effect of the source
charge(s). Source charges affect the way space behaves around them in two ways: 1) they
can create an electric field (which exerts forces) and 2) they can create an electric potential
field (which determines electric potential energy).
• The electric potential is defined by: Electric Potential =
• The potential difference between two points is frequently more useful than the absolute
potential (and easier to determine). Between two points in space, the potential difference is:
∆U
–W
∆V = q
= q (unit: 1 Volt = 1 J/C ) . For example, ∆U = q0 ∆V gives the change in
0
0
potential energy of a charge q0 when passed through a potential difference ∆V.
ΔV
. As an example, think about a positive
Δs
point source charge and a positive point test charge q0 . As the positive test charge moves
away from the positive source charge, the potential due to source charge decreases (∆V <0)
and E (>0) must point in the same direction as the displacement ∆s (away from the source
€
charge).
• Also, the electric field can be found from E = –
Section 20-2
• A charge placed between charged parallel plates possesses energy by virtue of its location,
because work must be done in order to place the charge at a particular distance from either
plate.
• For the positive charge in Example 20-2, the change in electric potential energy as q moves
from the positive to the negative plate is: ∆U = q ∆V = –q E ∆s. In this example, ∆V is
negative since V gets smaller as the negative plate is approached. Thus, ∆U is negative in
this example. The potential energy "given up" is converted into kinetic energy in this case.
• Note that the expression ∆U = –q E ∆s only holds for the specific case where E is constant.
You could apply this directly in Example 20-2, keeping in mind that if E and ∆s are in the
same direction, then ∆U will consequently be negative for a positive charge q.
Section 20-3
 k q
• The electric potential V  = 
for a point charge is a scalar. Electric potential has no
r
direction, only a magnitude which may be positive, negative, or zero. The net potential at
a point in space is the algebraic sum of the potentials due to each source charge (the signs
of the charges are included when calculating the net potential).
• Similarly the electric potential energy (a scalar) of two point charges is given by:
k q0 q
k q0 q
k q0 q
U = q0 V = r
. For point charges, ∆U = r
– r
.
B
A
Section 20-4
• "Equipotential" means "equal potential". Thus, an equipotential surface is a surface that has
the same value of potential everywhere on the surface. However, not all points that have
the same potential are necessarily on the same equipotential surface. An electric field line
always makes a right angle with an equipotential surface (regardless of the shape of the
equipotential surface).
• For an ideal conductor, every point on its surface (and in its interior) is at the same
potential. This means its surface is an equipotential surface and its interior is an
equipotential volume. Note that the expression E = –∆V/∆s then yields E = 0 inside the
conductor, since ∆V = 0 between any two points inside the conductor. This agrees with our
observations in section 19-6.
k q
= 4πk σ R predicts that smaller radius R
R
implies larger surface charge density σ. By extrapolation this means that charges (and
electric field lines) are concentrated near sharp points on conductors.
• For spheres with the same potential, V =
Section 20-5
• Definition Any pair of separated conductors that carry equal and opposite charge is called
a capacitor. This separation of charge means that there will be an electric field between the
conductors, a potential difference between the conductors, and energy stored in the electric
field of the capacitor. This ability to maintain a charge separation is called capacitance and is
Q
defined as the ratio of the charge stored to the potential between the plates: C = V
.
The unit of capacitance is the farad (F) = 1 Coulomb/Volt.
• For a parallel plate capacitor, the relationship between charge and potential difference is
 κ εo A
κ εo A
given by: Q =  d 
V = C V. Thus, C = d
= κ C0 for a parallel plate
capacitor. Typical capacitance sizes are in µF or pF.
• Dielectrics Capacitors with dielectric (insulating) material between their plates behave
differently from capacitors with vacuum between their plates. The relationships for an
Cd
Vo
Uo
E0
isolated capacitor are: κ = E
= C
= V
= U
,where κ is the dielectric
d
0
d
d
constant for a given type of material. Since κ ≥ 1, the presence of a dielectric must decrease
E, increase C, decrease V, and decrease the U stored compared to having vacuum between
the plates.
Section 20-6
• Energy Energy is stored in the electric field of a capacitor. The work done in charging a
capacitor (putting positive charge on one plate and negative charge on the other) is given
1
1
Q2
2
by U = 2
CV
= 2 QV = 2 C
. The energy density (energy per unit volume)
1
contained in the electric field between the capacitor's plates is given by: uE = 2
κ εo E2.