Physics 121: Electricity & Magnetism – Lecture 4
Carsten Denker
NJIT Physics DepartmentCenter for Solar–Terrestrial
Research
February 7, 2007 Center for Solar-Terrestrial Research
Electric Potential Energy
Gauss’ and Coulomb’s law are identical electrostatic force is a conservative force!
Electric potential energy
Reference configuration (initially infinite separation Ui = 0)
f iU U U W
U W
February 7, 2007 Center for Solar-Terrestrial Research
Electric PotentialPotential difference Potential
defined
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.
f if i
U U UV V V
q q q
f i
WV V V
q
WV
q
February 7, 2007 Center for Solar-Terrestrial Research
Equipotential Surfaces
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.
Equipotential surfaces are always perpendicular to electric field lines.
February 7, 2007 Center for Solar-Terrestrial Research
Calculating the Potential from the Field
Potential difference Potential difference with Vi = 0 at infinity
f
f i iV V E ds
f
iV E ds
February 7, 2007 Center for Solar-Terrestrial Research
Potential Due to a Point Charge
Point charge
Ensemble of point charges
A positively charged particle produces a positive electric potential. A negatively charged particle produces a negative electric potential.
0
1
4
qV
r
1 10
1
4
n ni
ii i i
qV V
r
February 7, 2007 Center for Solar-Terrestrial Research
Potential Due to a Continuous Charge Distribution
Line of charge
Charged disk
The component of in any direction is the negative of the rate of change of the electric potential with distance in that direction.
E
0
1
4
dqV dV
r
s
VE
s
x y z
V V VE E E
x y z
