Download Chapter 19: Electric Potential Energy and Potential

Chapter 19:
Electric Potential Energy and Potential
• Electric potential energy and potential
• Equipotential surfaces, electric field
• Omit 19.5 (capacitors and dielectrics)
1
Electrical potential energy
• A potential energy can be defined for a conservative force.
Example, gravity.
• For the electrostatic force:
– the work done in moving a charge from one place to another
is independent of the path taken
(no dissipation of energy by friction, etc)
⇒ The electrostatic force is conservative
⇒ An electrical potential energy can be defined...
2
Gravitational and Electrical Potential Energy
Change in PE from B to A is work
done in moving object from B to A
ΔPE = mg(hA − hB)
ΔPE = q0E(hA − hB)
3
Electric Potential Energy
Release the charge q0 from point A.
The electrostatic force does work, accelerates
the charge:
WAB = FΔs = q0EΔs = KEB − KEA
Conservation of energy:
Displacement = Δs
KEA + PEA = KEB + PEB
So, KEB − KEA = PEA − PEB = q0EΔs
4
WAB = PEA − PEB = q0EΔs
Write:
PEA = q0VA, PEB = q0VB
VA,B = electrical potential (volts)
Then, PEA − PEB = q0(VA −VB) = q0EΔs = WAB
WAB
(volts)
q0
VA −VB
ΔV
E=
=−
Δs
Δs
VA −VB =
Unit: N/C or V/m (equivalent)
• If ΔV = 0, the potential energy of charge q0 is constant and
E = 0 in the direction from A to B.
• The line from A to B is then an “equipotential” line.
19.2
5
Prob. 19.2
An electric force moves a charge of q = 1.8 × 10-4 C from A to B and
performs 5.8 × 10-3 J of work on the charge.
a) What is PEA – PEB ?
b) What is VA – VB ?
c) Which point has the higher potential?
6
Equipotentials and
electric field
V1
All points between B and C on the
blue line are at the same potential
⇒ a charge has constant PE on the
blue line (same q0V1)
V2
⇒ no work is done in moving the
charge from B to C along the
equipotential
⇒ The electric field (red lines)
points in a direction at right
angles to the equipotentials.
A conductor is an equipotential volume
E = 0, V = constant throughout
7
Electric field and equipotential surface
E must be
perpendicular to
equipotential!
If the electric field is not perpendicular to the equipotential surface, then
there is a component parallel to it, so work would have to be done to move
a charge along the surface – which would no longer be an equipotential!
8
Equipotentials and Field Lines
E
E
V
V
V=0
9
ΔV
E =−
Δs
Capacitor
10
Prob. 19.56
The four outer points are all 6 mm from the origin.
Find the electric field at the origin.
19.32
11
Potential Energy
Potential energy of 1 electron charge at a potential of 1 V.
PE = qV = eV = (1.6×10-19 C)×(1 V) = 1.6×10-19 J
or, PE = 1 eV (electron-volt)
1 eV = 1.6×10-19 J
As the charge moves, ΔKE = –ΔPE
(i.e., KE + PE = constant)
An electron charge gains a kinetic energy of 1 eV in falling
through a potential drop of 1 V.
19.6
12