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 2002
Physics 217, Fall 2002
1
Curvilinear coordinates
Co
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 components Vector transformation Second-rank tensors
4 Septem
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 2002
E
2Q
-2Q
1
Capacitance
Consider two conductors,
ch
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 its
potential
Poissons and Laplaces
equations
23 Septembe
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
Inconsistency?
Non-superposition of
potential energy
25 September 2
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 Law
for gravity.
x
20 September 2002
dE
dq = da
r
da =
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=
s
s s s
2
+
4 October 2002
1 2V
2
s
Physics 217, Fall
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 Purcell, chapter 2, for more
information.
S2
B
dl1
=
S1