Week 3:
Chapter 24
Gauss’s Law
Gauss’ Law
Gauss’ Law can be used as an alternative procedure for calculating electric
fields.
Gauss’ Law is based on the inverse-square behavior of the electric force
between point charges.
It is convenient for calculating the electric field of highly symmetric charge
distributions.
Gauss’ Law is important in understanding and verifying the properties of
conductors in electrostatic equilibrium.
Introduction
Electric Flux
Electric flux
is the product of the
magnitude of the electric field and the
surface area,
A
, perpendicular to the
field.
Φ
E
=
EA
Units:
N · m
2
/ C
Section
24.1
Electric Flux, General Area
The electric flux is proportional to the
number of electric field lines penetrating
some surface.
The field lines may make some angle
θ
with the perpendicular to the surface.
Then
Φ
E
=
EA
cos
θ
Section
24.1
Electric Flux, Interpreting the Equation
The flux is a maximum when the surface is perpendicular to the field.
θ
= 0
°
The flux is zero when the surface is parallel to the field.
θ
= 90
°
If the field varies over the surface,
Φ
=
EA
cos
θ
is valid for only a small
element of the area.
Section
24.1
Electric Flux, General
In the more general case, look at a
small area element.
In general, this becomes
The surface integral means the
integral must be evaluated over the
surface in question.
In general, the value of the flux will
depend both on the field pattern and on
the surface.
cos
E
i
i
i
i
i
E
A
θ
E
A
0
surface
lim
i
E
i
i
A
E
E
A
d
E
A
Section
24.1

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