Physics 121: Electricity &
Magnetism – Lecture 4
Carsten Denker
NJIT Physics Department
Center for Solar–Terrestrial Research
Electric Potential Energy
Gauss’ and Coulomb’s law are
identical  electrostatic force
is a conservative force!
U  U f  U i  W
Electric potential energy
U  W
Reference configuration
(initially infinite separation
 Ui = 0)
February 7, 2007
Center for Solar-Terrestrial Research
Electric Potential
Potential difference
Potential defined
U i U
V  V f  Vi 


q
q
q
Uf
W
V 
q
W
V  V f  Vi  
q
Electric potential is a property of an electric field, regardless of whether
a charged object has been placed in that field. It is measured in J/C or V.
Electric potential energy is an energy of a charged object in an external
electric field (or more precisely, an energy of the system consisting of
the object and the external field. It is measured in J.
February 7, 2007
Center for Solar-Terrestrial Research
Equipotential Surfaces
Equipotential
surfaces are
always
perpendicular
to electric
field lines.
Imaginary or real, physical surface where
adjacent point have the same electric
potential.
No work is done by the electric field on a
charged particle while moving the particle
along an equipotential surface.
February 7, 2007
Center for Solar-Terrestrial Research
Calculating the Potential from the Field
Potential difference
f
V f  Vi   E  ds
i
Potential difference
with Vi = 0 at infinity
f
V   E  ds
i
February 7, 2007
Center for Solar-Terrestrial Research
Potential Due to a Point Charge
Point charge
1 q
V
4 0 r
Ensemble of point
charges
n
1 n qi
V  Vi 

4 0 i 1 ri
i 1
A positively charged particle produces a
positive electric potential. A negatively
charged particle produces a negative
electric potential.
February 7, 2007
Center for Solar-Terrestrial Research
Potential Due to a Continuous
Charge Distribution
Line of charge
V   dV 
1
dq
4 0  r
Charged disk
V
Es  
s
V
Ex  
x
V
Ey  
y
V
Ez  
z
The component of E in any direction is the negative of the rate of
change of the electric potential with distance in that direction.
February 7, 2007
Center for Solar-Terrestrial Research