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Electric Potential
Electric Potential:
U
V
q
or
U  qV
Units: 1 volt V = 1 joule/coulomb
•V is a SCALAR
•V is determined to within an arbitrary constant.
•We can choose to set V=0 at any position (most
often at “r=infinity”)
•There is no absolute potential
Rule: Electrostatic field lines always point to decreasing
electric potential. Why?
Note: electric potential V is not the same as electric
potential energy U !!
potential energy
V 
charge
What does a potential difference of 1 volt mean?
1 Volt= 1J/C
It means one joule of work needs to be done to
move one coulomb of charge through a potential
difference of one volt.
This work could be negative or positive depending
on the sign of the charge and whether the field or us
does the work and whether the charge moves from a
higher to a lower potential or vice-versa.
Electric Potential
(not the same as electric potential energy)
“Test charge” +q moves
A small displacement ds
B
E
ds
q +


F  qE
A
Find: element of work dW done by the field.
Recall…
dW  F  ds  qE  ds
The work is proportional to the charge.
The electric force is conservative, so we can
define an electrostatic potential energy U for the
charge in the electric field such that:
dW
field
 dU
We then define electric potential difference dV by
dU  qdV
so that
dV = - E •ds
Note: dV does not depend on the charge q. It only
depends on the field and a displacement in the field.
When the field does work on the test charge,
electrostatic potential energy is converted to
other forms of energy, such as kinetic.
Eg: a charge q of mass m starts from rest in a field E.
What will its kinetic energy be after it moved a
distance d in the field ?
W=Fd=qEd
W=∆K= ½ m∆v2
Eg: Point a is at 5V and point b is at 10V. The charge
moved is +3C.
a) How much work is done by the field moving the
charge from a to b?
b) How much work is done by the field moving the
charge from b to a?
c) How much work is done by us moving the charge
from a to b?
d) How much work is done by us moving the charge
from b to a?
recall : W  U
W  U
field
us
Example:
Find V to accelerate electrons to 107 m/s.
e  1.60 x1019 C and me  9.11x 10 31kg
V2
V1
v1  0
-
v 2  1x 107 m s
“Electron Volt”
• A unit of energy.
(eV):
Recall U=qV
1 joule = 1 coul-volt and 1 C = 6.2x1019 e, so
1 J= 6.2x1019 eV. Therefore
1 eV  1.6x10-19J
The unit eV is useful for energy levels in an atom
“EQUIPOTENTIALS”
• Are surfaces on which V = constant
• Are always perpendicular to the electric field
• A conductor is always an equipotential (if no
current inside it)
• Closely spaced equipotential surfaces implies
large E
• Widely spaced equipotential surfaces implies
weak E
Uniform Electric Field:
q
a
Higher
Potential V
Work we do is:

s
+
b


F
b
Wus  U  qV
 q(V (b)  V (a))

E
Lower
Potential V
Quiz: A conductor with charges in static equilibrium on it
has constant potential on its surface and interior.
Recall, E=0 inside. So the surface of the conductor is
an equipotential surface.
V=5V
V=5V
Inside too
V=5V
V=5V
What is the sign of charge, if any, on the surface of the
conductor?
A) positive
B) negative C) zero D) need more info !
New unit for electric field:
Recall that
dV = - E •ds
So unit for E is V/m which we can use instead of N/C.
Finding E given electric potential:
In one dimension, given V(x), using the result above we get:
dV
E 
dx
x
For example, find E at x=2m when
V(x)=2+3x-x2 volts
Example:
+
2 mm
20V
a) Find electric field strength between plates
b) Sketch a few equipotential surfaces
Summary: Electric Potential
potential energy
V 
charge
U  qV
dV
E 
dx
x
Wus  U  qV
W field  U   qV