Physics 121: Electricity & Magnetism – Lecture 3

Carsten Denker

NJIT Physics DepartmentCenter for Solar–Terrestrial

Research

January 31, 2007 Center for Solar-Terrestrial Research

Coulomb’s Law and Flux

Gauss’ law relates the electric fields at a point on a (closed) Gaussian surface and the net charge enclosed by that surface.

Gauss’ law uses symmetry and is fully equivalent to Coulomb’s law.

Which one you have to use depends on the application!

cosv A cosvA v A

January 31, 2007 Center for Solar-Terrestrial Research

Flux of an Electrical Field

Electric flux through a Gaussian surface

discrete form

integral form

The electric flux through a Gaussian surface is proportional to the number of field lines passing through that surface.

E A

E dA

January 31, 2007 Center for Solar-Terrestrial Research

Gauss’ Law

Gauss’ law

Gauss’ law

Gauss’ law and Coulomb’s law

0 encq

0 encE dA q

0 0 enc

20 0

20

4

1E=

4

E dA E dA q

E dA E r q

q

r

January 31, 2007 Center for Solar-Terrestrial Research

A Charged Isolated Conductor

If an excess charge is placed on an isolated conductor, the amount of charge will move entirely to the surface of the conductor. None of the excess charge will be found within the body of the conductor.

Conducting surface

0

E

January 31, 2007 Center for Solar-Terrestrial Research

Cylindrical and Planar Symmetry

Planar symmetryCylindrical symmetry

02E

r

02

E

January 31, 2007 Center for Solar-Terrestrial Research

Spherical Symmetry

Spherical shell

Uniform charge (field at r R)

A shell of uniform charge attracts or repels a charged particle that is outside the shell as if the shell’s charge were concentrated at the center of the shell.

A shell of uniform charge exerts no electrostatic force on a charged particle that is located inside the shell.

20

1

4

0

qE r R

r

E r R

30

1

4E r

R