Lecture 7 Notes: Curvilinear Coordinates
So exactly what is curvilinear?
And whats this orthonormal stu?
(=1?)
Gradient in Spherical
Let f (x) = f (r, , )
df =
f dx
= f (e dr + e rd + e r sin d)
=
dr +
dr
d
d +
d
d
So ,
f = e
dr
+ e
+ e
r d
r sin d Diverg
Lecture 4 Notes: Divergence
Dot Operator
dT =
x
=
dx +
y
dy +
z
dz
T dl
T
=
0 stationary point
T
x
T
=
T
T
y z
Whats T ? A scalar function of a vector (usually , sometimes )
T = T (x, y, z)
(x, y, z) charge density
V (x, y, z) = (x, y, z) electric potent
Lecture 5 Notes: Integral Calculus
b
dx = f (b) f (a) b
dx
(T ) dl = T (b) T (a)
a
a
(T ) dl =
a
dT
v(x) dl is pathindependent i v(x) = f (x) .
1
4
x E
=
(x )r
4
d3 x = E(x)
(x )
) 3
d x 4
xx 

(x )
= (
)d3 x
x xx 3
1
=
(x ) 3 (x x )
3
dx 0
=
0
Lecture 3 Notes: Vector Review
E(z) =
4
(xi +
L (x2 +z 2 )3/2
zj)dx
=
4
(x2 +z 2 )1/2 L
Dimensionless Integrals
+ .
u = x2 + z 2
du
=
2xdx x =
z tan
dx = z sec2 d
L
L
L3
0 (z 2 +l2 )3/2
dl
1
(L2 L2 +L2 L2 )3/2
d( l )
Vector
 a sequence of numbers (a1,
Lecture 10 Notes: Electric Potential
Electric Potential
E(x)
=
=
V
1
4
V
(x)d3 x
xx 
V (x)
=
Vx0 (x) is work done to move charge from x0 to x.
Find V on xyplane.
(Hint: cylindrical
coordinates)
V (x)
=
V (r, , z) =
V (r, , 0) =
1
4
l
l
dz
r 2 +z 2
z
Lecture 9 Notes: Line and Plane Charges
Given line of charge with density x
Line Charge
Find E(r) everywhere
E da = 1
Qenclosed
Qenclosed
L2r E(r) =
= L
S
0
L
0
E(r) =
2 r
r
No because E = 0.
No z because vectors cancel out
E(r)
r
Like a plane : Cross se
Lecture 8 Notes: Applications of Gausss Law
What is the EField on the axis of a circular loop of a uniformly
charged thin wire with total charge q?
dEz = dE cos =
dE a2 +z2
1
40
E(z) =
=
=
=
2
1
4
q
0 2a
dq
C r3
(cos i+sin j+zk)
(a2 +z 2 )3/2
0
4
qz
0
Lecture 1 Notes: Intro to Electrostatistics
Coursework 3 hour exams and one nal
Problem sets due in class on Tuesdays
E/M Electromagnetic Forces
Force Interaction Particles
matter/energy
Gravity
most particles
Weak
E/M
photons
Strong
quarks , gluons
ab