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Unformatted text preview: Planar Geometry
E must be normal to surface (no preferred direction) E is the same on each side (no preferred side) Gaussian surface is any shape with constant cross sectional area A
S S E dA = qenc
0 Gauss’ law LHS RHS E is constant E d A = EA + EA = 2 EA q enc = A E= 2 0
PHY2049: Chapter 23 23 Non-Infinite Plane
For a non-infinite plane and a point a distance z away, this formula is a very good approximation when
z is small compared to the dimensions of the plane z is small compared to the distance from the edges Consider a charged disk of radius R (Chap. 22, p.591)
Find E at a distance z about the center of a charged disk E=
z z z z = = = = 2 1
0 z z 2 + R2 = 0.99 EGauss = 0.95 EGauss = 0.90 EGauss = 0.55 EGauss
PHY2049: Chapter 23 24 0.01R 0.05R 0.10R 0.50R Eexact Eexact Eexact Eexact Conductors
Basic laws about conductors (proved in class and P. 613). These are true for electrostatic equilibrium and for a continuously connected conductor
E = 0 inside a conductor All charges appear on surface of conductor, not interior On the conductor surface, E field is normal to surface No charge appears on any interior cavity surface Things are different when we consider currents in Ch. 26
Because conductor is not in electrostatic equilibrium PHY2049: Chapter 23 25 Spherical Conducting Shells
Point charge of size +Q inside a neutral conducting shell
From Coulomb’s law we expect to see some – charge on inner surface of shell and some + charge on outer We can prove that there is exactly –Q charge on inner surface Draw Gaussian surface just inside conducting shell
E = 0, so total of 0 enclosed charge +Q at center, so must be –Q on inner surface Thus there is +Q on outer surface Easily generalize to multiple shells, putting net charge on each shell +Q Gaussian surface
PHY2049: Chapter 23 26 ...
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This note was uploaded on 02/12/2010 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
- Spring '08