1 Physics 202, Lecture 4 Today’s Topics More on Gauss’s Law Electric Potential (Ch. 23) Electric Potential Energy and Electric Potential Electric Potential and Electric Field Gauss’s Law: Review ! E = ! E i d ! A " " = q encl # 0 Use it to obtain E field for highly symmetric charge distributions. Method: evaluate flux over carefully chosen “Gaussian surface” spherical cylindrical planar (point charge, uniform sphere, spherical shell,…) (infinite uniform line of charge or cylinder…) (infinite uniform sheet of charge,…)
7
Embed
More on Gauss’s Law Electric Potential (Ch. 23) Electric Potential … · 2008-01-31 · 1 Physics 202, Lecture 4 Today’s Topics More on Gauss’s Law Electric Potential (Ch.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
Physics 202, Lecture 4
Today’s Topics
More on Gauss’s Law
Electric Potential (Ch. 23) Electric Potential Energy and Electric Potential Electric Potential and Electric Field
Gauss’s Law: Review
!E =!Eid!A"" =
qencl
#0
Use it to obtain E field for highlysymmetric charge distributions.
Method: evaluate flux over carefully chosen “Gaussian surface”
spherical cylindrical planar
(point charge, uniform sphere, spherical shell,…)
(infinite uniform line of charge or cylinder…)
(infinite uniform sheetof charge,…)
2
Spherical Symmetry: Examples
Spherical symmetry: choose a spherical Gaussian surface, radius r
Then:
Example 1 (last lecture): uniformly charged sphere (radius a, charge Q)
E =qencl
4!"0r2
!Eid!A"! = E4"r2 =
qencl
#0
!Er>a
=Q
4!"0r2r
!Er<a
=Qr
4!"0a3r
Example 2: Thin Spherical ShellFind E field inside/outside a uniformly charged thin
spherical shell, surface charge density σ, total charge q
Gaussian Surfacefor E(outside)
Gaussian Surfacefor E(inside)
Er<a
= 0Er>a
=q
4!"0r2
qencl = 0qencl = q
Trickier examples: set up(holes, conductors,…)22.29-31, 22.54 (board)
Kinetic Energy (K). Potential Energy U: for conservative forces(can be defined since work done by F is path-independent)
If only conservative forces present in system,conservation of mechanical energy: constant
Conservative forces: Springs: elastic potential energy Gravity: gravitational potential energy Electrostatic: electric potential energy (analogy with gravity)