Gauss's Law
Study Guide
There will be a Gauss's law question on the final exam.
Section 24.1: Electric Flux
Electric flux represents the total number of electric field lines crossing through a surface. The
basic equation for flux is
FI œ IE
where I is the magnitude of the electric field, and E is the area of the surface.
t pointing straight out. There
The equation above only works for a flat surface and a constant E
are several more complicated versions:
t points straight into the surface, then the flux is negative:
1. If E
FI œ IE
t is parallel to the surface, then the flux is zero.
2. If E
t makes an angle with the surface, then
3. If E
t œ IE cos )
t†A
FI œ E
t is the area vector.
where A
4. If the surface has several parts, then you must add together the flux from each part.
The most general formula for flux is:
FI œ (
t
t † .A
E
surface
t-field passing through any surface. In practice, we always use one
This equation applies to any E
of the simpler rules for flux given above.
Problems: 1, 3, 4
Answers: 4. (a) #,$%! N † m# ÎC
(b) #,$%! N † m# ÎG
(c) !
Section 24.2: Gauss's Law
Gauss's law states that the total electric flux out of a closed surface is proportional to the amount
of charge inside:
FI œ
Uinside
%!
You may use Gauss's law on any closed surface, even a surface that you make up. In general,
if you want to figure out how much charge there is in a region, you can surround it with a surface
and then apply Gauss's law.
Problems: 6, 7, 9, 12, 17
Answers: 6. (a) &&Þ( nC
(b) very little
12. "Þ(( pCÎm$
Charge Density
You may want to review the definitions of charge density given in section 23.5:
• Volume charge density is charge per unit volume.
• Area charge density is charge per unit area.
• Linear charge density is charge per unit length.
Problems: Chapter 23 # 30
Answers: 30. (a) #!! pC
(b) "%" pC
(c) &)Þ* pC
Section 24.3: Applications of Gauss's Law
Though you do not need to know most of the formulas in this section, reading through the
examples may help you to understand how to apply Gauss's law. The only really important
equation in this section is the formula for the electric field produced by a plane of charge:
I œ
5
#% !
Here 5 is the charge per unit area on the plane (i.e. the surface charge density).
Section 30.5: Gauss's Law in Magnetism
Since there is no such thing as magnetic charge (as far as anyone knows), the total magnetic flux
through a closed surface must be zero:
FF œ !
Problems: Chapter 30 # 39
(for a closed surface)