B dA 0 From lab …
Faraday’s Law of Induction
Vs EMF N s
BP
dB
d
d
BP As N s As cos P
B
dA
N
P
s
dt
dt
dt
o iP N P
2rP
oVP N P
2rP RP
o N P
2rP RP
VP peak sin(t )
Things you can prove
with Gauss’ Law:
The two shell theorems
For a uniform, spherical charge distribution …
For a uniform spherical charge distribution …
Properties of conductors:
Any excess charge on a conductor …
The electric field inside the bulk of a
conductor is always …. A perfect conductor …
is an equipotential surface & throughout!
has all excess charge on its outer surface.
has no internal E field (does this make sense
based on first statement, above?).
does not necessarily have a uniform charge
distribution on its surface.
has a field just outside its surface that is
perpendicular to the surface.
Some of these ideas are very important in circuit analysis!
Electric Field due to a point charge
within a conducting spherical shell
Spherical shell is electrically neutral
Charges that make up conducting
sphere are free to move about in
response to field created by point
charge at center
Those charges arrange themselves
in such a way that the field they
create cancels out the field due to
the point charge (within the
conducting material)
So, the field in the conductor is
zero!!!! For Example:
A small charged ball lies within the hollow of a
metallic spherical shell of radius R. Here, for
three situations, are the net charges on the ball
and the shell, respectively:
(1) + 4q, 0
(2) – 6q, +10q
(3) +16q, -12q
Rank situations according to the charge on the
(A) inner surface of the shell and
(B) the outer surface of the shell,
most positive first.
Gauss' Law for Magnetism
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