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F16 PH 333 2.1.1-2.1.4

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Richard Datwyler

on 1 October 2018

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Transcript of F16 PH 333 2.1.1-2.1.4

Electrostatics
The electric field
2.1.1 Introduce electrostatics
2.1.2 Coulomb's Law
2.1.3 The Electric Field
2.1.4 Continuous Charge Distributions

Electrostatics
Main principles
Electrostatics = Source charges are stationary
Charges exert forces on other charges
Superposition for multiple charges
Moving charges more complicated
Coulomb's Law
Force on a test charge Q from a stationary charge q a distance of r away.
tricky bits
R hat. This is a vector and it points either towards or away from the source charge.
R. It is the vector that points from the source charge to the test charge.
Quiz!
The Electric Field
From the principle of Superposition, there is only one E field.

Note is a function of position r. (buried in the r hat)
What is it? Think of it as a field.
Continuous distribution of charge
Tricky bits
dq: either line, surface or volume charge densities.
R hat: has the vector direction part. Needs to be in the units of integration.
R : is the length of the vector pointing from each little source charge element to point of interest.
2
Continuous Distributions
These change the integral
Note:
Depend upon the integration variable
And it can be variable
Line Charge
p
r
E
r` = x
x
z
0
Consider a line of charge, 2L, on x axis, what is the E field at pt. Z above the midpt.
Find
dq
symmetry, Z direction only, needs
R
R hat
Line Charge
p
r
E
r` = x
x
z
0
Collect
Binomial expansion
What happens when z>>L or L>>z ?
for 1>>x
for z>>L
how about L>>z
1 of the 5 charges has been removed, as show. What's the E field at the center?
a) +(kq/a ) j
b) -(kq/a ) j
c) 0
d) Something entirely different!
e) This is a nasty problem
Practice
Gut feeling ?!?
Prove it!
Do you dare find this?
(not in this coordinate system)
"Can you go over different charge distribution integrals with us (line, surface, and volume)?
"I don't think that I fully understand why they split the problem up in example 2.1"
Ring charge
"why is electric force not an action at a distance force"
E field
What is the E field from a ring of charge with uniform charge density lambda, having radius a and at position z?
Disk Charge?
z
a
find:
dq
R
Rhat
Full transcript