1. TOPIC 3 Gauss’s Law

2. Introduction From last lecture:
Electric field strength is equal to the density of field lines
Number of lines starting on a charge is proportional to the charge
Gauss’s Law relates flux (= flow of field lines) through a closed surface to total charge enclosed
Very useful for calculating field, especially for symmetric charge distributions.

3. Electric Flux Consider surface, area A, in uniform field E
Flux  is field  projected area  = E A cos
Can also consider this as area  normal component of field.
Define vector A, magnitude proportional to area, direction of normal to the surface.
 = E.A

4. For non-uniform field:
Note: lines passing one way through surface give positive contribution to , other direction negative.
Continuous lines 
net flux through closed surface = 0

5. Consider spherical Gaussian surface around point charge:
By Coulomb’s Law: So
What about a different shape surface?
Net flux through combined dotted and dashed surfaces = 0.
Flux through any surface surrounding Q is Q/0.

6. Gauss’s Law
The net flux through any closed surface around a total charge Qtot is just Qtot/0.
Using Gauss’s Law to determine the field:
Use the symmetry of the charges to determine the pattern of field lines.
Choose a Gaussian surface which is locally either parallel to E or perpendicular to it.
Where E is parallel to dA, E is locally constant.

7. Example 1
Show that when an isolated conductor carries a charge, it must reside only on the surface.
Example 2
Show that the field about a charged conducting sphere is identical to that about the same charge concentrated at the centre of the sphere.
Example 3
A charge Q is distributed uniformly throughout an insulating sphere of radius R. What is the electric field at points (a) outside the sphere (b) inside the sphere?

8. Example 4
An infinite sheet carries a surface charge density . What electric field does it produce?
Example 5
An infinitely long wire carries a linear charge density . How does the electric field it produces vary with distance from the wire?