# GAUSS'S LAW FOR SYMMETRIC CHARGE DISTRIBUTIONS ...

Ηλεκτρονική - Συσκευές

13 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

94 εμφανίσεις

GAUSS’S LAW FOR SYMMETRIC CHARGE DISTRIBUTIONS (19.10)

Recall Gauss’s Law:

0
inside
surface
closed
over
e
ε
q

r
r

r
is a vector normal to surface with magnitude equal to the area of the surface
element

How do we use Gauss’s Law? Two Ways:

0
inside
e
ε
q

o relates flux to charge inside for surface of ANY shape

0
inside
surface
closed
over
ε
q

r
r

o gives a way to calculate
E
r
⁦潲 SPECIAL cases

 mostly useful if we normal component of
E
r
⁩猠捯湳瑡湴⁯癥爠灡牴⁯映

Using Gauss’s law to calculate Electric Field
E
r

• Must know direction of electric field from symmetry of problem

o radial (spherical symmetry) for point charge

o radial (cylindrical symmetry) for a long line of
charge

o uniform for a large flat sheet of charge

• Must choose Gaussian surface that allows us to calculate

⋅=Φ
surface
closed
over
e
r
r

o Must be able to factor
E
r
⁯畴⁯映flux integral in region of space where we
want to find electric field

Two cases for which we can evaluate

surface
r
r
for all or part of surface

E
r
uniform and perpendicular to part or all of Gaussian surface

o then flux is

n
r
r
for that part of the surface

E
r
parallel (tangent) to part of the Gaussian surface

o then
r
r
for that part of surface → no contribution to total flux
EXAMPLE:
(a) Find the electric field INSIDE and OUTSIDE of a uniformly charged
insulating sphere with radius a and total charge Q.
(b) Plot the magnitude of
E
r

(c) Calculate the electric potential
(
)
rV
inside and outside the sphere.

1st: Look at
ar<
(inside of sphere)
• Draw Gaussian surface, radius r, same centre
• By symmetry,
E
r
is

⁴漠䝡畳獩慮⁳畲晡捥⁥癥特睨敲攠
• Normal component
n
E
is uniform over the surface

2nd: Look at
ar>
(outside of sphere)
• Draw Gaussian surface, radius r, same centre
• By symmetry,
E
r
is

⁴漠䝡畳獩慮⁳畲晡捥⁥癥特睨敲=
• Normal component
n
E
is uniform over the surface
EXAMPLE:
What is the magnitude of the electric field at a perpendicular distance r from
an infinitely long, uniformly charged rod with charge per unit length of
λ

=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
EXAMPLE:
What is the magnitude of the electric field near an infinitely large, uniformly
charged plane with charge per unit area of
σ

=
=
=