Last Lecture

1
Last Lecture Gausss law Using Gausss law
for spherical symmetry This lecture Using
Gausss law for line symmetry plane
symmetry Conductors in electric fields
2
Coulombs law tutorial Consider two positively
charged particles, one of charge q0 (particle 0)
fixed at the origin, and another of charge q1
(particle 1) fixed on the y-axis at (0, d1,
0). What is the net force F on particle 0 due to
particle 1?   Express your answer (a vector)
using any or all of k, q0, q1, d1, x-hat, y-hat,
and z-hat. Answer F  
( )
3
Part B What is the new net force on particle 0,
from particle 1 and particle 2? Answer F
 
Here is an example of a wrong answer - just a
careless mistake.
This one presumably meant to put a bracket
around the two terms, but didnt.
4
Part D What is the net force on particle 0 due
solely to this charge 3? Answer F
The answer here was close but still missing a
factor of ½. The message is that accuracy
matters.
5
A
B
C
D
E
These are two-dimensional cross sections through
three dimensional closed spheres and a cube.
Which of them has the largest flux through
surfaces A to E? Which has the smallest flux?
6
Example 21.2 Field of a hollow spherical sphere
From Gausss law, E 0 inside shell
Example 21.3 Field of a point charge within a
shell Done on board Read TIP SYMMETRY MATTERS!
7
Line symmetry Example 21.4 Field of a line of
charge
A section of an infinitely long wire with a
uniform linear charge density, ?. Find an
expression for E at distance r from axis of wire.
8
Applying Gauss Law cylindrical symmetry
(Compare this result with that obtained using
Coulombs law in Example 20.7, when wire is
infinitely long.)
9
Plane symmetry Example 21.6 Field of an infinite
plane sheet of charge p 357
10
Applying Gauss Law planar symmetry
A thin, infinite, nonconducting sheet with
uniform surface charge density Find E at
distance r from sheet.
11
Electric field due to plane of charge is
12
CHECKPOINT The figure shows two large parallel,
nonconducting sheets with identical (positive)
volume charge density. Rank the four labelled
points according to the magnitude of the net
electric field there, greatest first.
A
B
C
D
Answer C, D equal B A
13
21.5 Fields of arbitrary charge distributions
14

• CHECKPOINT There is a certain net flux ?I
  through a Gaussian sphere of radius r enclosing
  an isolated charged particle. Suppose the
  Gaussian surface is changed to
• (a) a larger Gaussian sphere,
• (b) a Gaussian cube with edge length equal to r,
  and
• (c) a Gaussian cube with edge length 2r.
• In each case is the net flux through the new
  Gaussian surface
• greater than
• less than, or
• equal to ?I ?

Answers all equal as charge enclosed is the same
15
When we must use Coulomb - no symmetry!
Find E at point P due to a finite line
charge Charge Q is uniformly distributed on a
straight line segment of length L. Choose axes
and draw diagram Write expression for dE due to
dq Find dEy Integrate to find Ey (what are the
limits?) Substitute trigonometric formulae Repeat
for Ex
16

• True or False?
• If the net electric flux out of a closed surface
  is zero, the electric field must be zero
  everywhere on the surface.
• If the net electric flux out of a closed surface
  is zero, the charge density must be zero
  everywhere inside the surface.
• The electric field is zero everywhere within the
  material of a conductor in electrostatic
  equilibrium.
• The tangential component of the electric field is
  zero at all points just outside the surface of a
  conductor in electrostatic equilibrium.
• The normal component of the electric field is the
  same at all points just outside the surface of a
  conductor in electrostatic equilibrium.

True A
False F
False
False
True
True
False