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F16 PH 333 2.1.1-2.1.4
Transcript of F16 PH 333 2.1.1-2.1.4
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 = Source charges are stationary
Charges exert forces on other charges
Superposition for multiple charges
Moving charges more complicated
Force on a test charge Q from a stationary charge q a distance of r away.
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.
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
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.
These change the integral
Depend upon the integration variable
And it can be variable
r` = x
Consider a line of charge, 2L, on x axis, what is the E field at pt. Z above the midpt.
symmetry, Z direction only, needs
r` = x
What happens when z>>L or L>>z ?
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
d) Something entirely different!
e) This is a nasty problem
Gut feeling ?!?
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"
"why is electric force not an action at a distance force"
What is the E field from a ring of charge with uniform charge density lambda, having radius a and at position z?