Today in Physics 217: the divergence and curl
theorems
dl2
Flux and divergence:
proof of the divergence
theorem, l Purcell.
Circulation and curl: proof
of Stokes theorem, also
following Purcell.
See P
Today in Physics 217: Laplaces equation
Solutions to the Laplace
equation
Simple examples
Uniqueness of solutions
1 2 V
V= 2
r
r
r
r
V
1
+ 2
sin
r sin
2
+
2V
1
2
2
r sin
2
=0
1 V
V=
Today in Physics 217: charged spheres
Finish example from
Wednesday.
Field from a charged
spherical shell,
z
calculated with
Coulombs Law.
Same, calculated with
Gauss Law.
Analogy with
gravity: Gauss
Today in Physics 217: work and energy in
electrostatics
Last spherical example:
potential from a
uniformly-charged
spherical shell
Work and potential
energy
Electrostatic potential
energy
Inconsistenc
Today in Physics 217: electric potential
Finish Fridays discussion
of the field from a
uniformly-charged sphere,
and the gravitational
analogue of Gauss Law.
Electric potential
Example: a field and it
Today in Physics 217: capacitance
Capacitance and
capacitors
Energy storage in
capacitors
Example calculations of
capacitance
Units
Capacitors, work and
stored energy
2 October 2002
Physics 217, Fall
Today in Physics 217: vector analysis
Vectors: have direction have magnitude Vector operations include vector addition vector multiplication by a scalar the dot product the cross product Vector compon
Today in Physics 217: more vector calculus
z
Vector derivatives in
curvilinear coordinate
systems: spherical and
cylindrical coordinates.
The Dirac delta function.
r
r
y
x
z
z
s
z
s
y
x
13 September 2