Transcript EQUIVALENT Gauss`s Law

Gauss’s Law
AP Physics C
How to use Gauss’s Law
Count the lines leaving a surface as +
 Count the lines entering a surface as –
 Figures 23-10 and 23-11 on p.696

Gauss’s Law
Relates the electric field on a closed
surface to the net charge within the
system
 For static charges, Gauss’s Law and
Coulomb’s Law are EQUIVALENT
 Gauss’s Law: The net number of lines
leaving any surface enclosing the
charges is proportional to the net charge
enclosed by the surface

Electric Flux Φ
The mathematical quantity that
corresponds to the number of field lines
crossing a surface
 For a surface perpendicular to the
Electric Field, the flux is defined as the
product of the magnitude of the field E
and the area A:

Φ = EA (units are Nm2/C)
The box may enclose a charge, by placing a test charge and
observing F, we know E. It is only necessary to do this at the
surface of the shape.
Pictures of
outward (+)
flux and
inward (-)
flux
Electric Flux Φ continued

When the area is NOT perpendicular to
E, then the following equation is used:
Φ = EAcosθ = EnA
Where En is the component of E that is
perpendicular or normal to the surface
Flux


Flux, in this case Electric Flux, is the amount of
(electric) field passing through a specified area.
Think of water flowing in a pipe (flux comes from
the Latin for “flow”)
Situations where the total flux equals zero
Ф = 0 through triangular prism below.
E = 500 N/C
50 cm
30 cm
40 cm
40 cm
The E-field decreases at 1/r2 while the area
increases at r2 and that increase and decrease
cancel each other out and that is why the size of
the surface enclosing Q does not matter.
Electric Flux Φ continued
What if E varies over a surface? (see Fig
23-14 on p.697)
 If we take very small areas A that can be
considered a plane, we can then sum the
fluxes for each area using Calculus

Flux
Symbol ФE
 Unit  Nm2/C
 Equation:

 
 E  E  A  EA cos 
 
 E   E  dA
Quantitative Statement
of Gauss’s Law
P698
 The net flux through any surface equals
4πk times the net charge inside the
surface

Gauss’ Law
E 
 E  dA 
Qenclosed
0
 4 kQenclosed
What we can conclude about Ф
1.
2.
3.
Ф is proportional to q
Whether Ф is inward or outward
depends on the q inside the surface
A q outside the surface offers zero Ф
because Фin = Фout
Point Charge
Line of Charge
Sheet of Charge
Uniformly charge insulator at a varying
r