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