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P16 PH 333 2.3.1-2.3.5

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Richard Datwyler

on 3 October 2018

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Transcript of P16 PH 333 2.3.1-2.3.5

Electric Potential
2.3.1-2.3.5
2.3.1 Introduce the potential
2.3.2 Principles of the potential
2.3.3 Poisson's and Lapace's equ.
2.3.4 Potentials from charge distributions
2.3.5 Boundary conditions
Electric Potential
Note it is a scalar, much easier to deal with (no directions), units are volts.
V from E and E from V
Issue with the reference point.
It just adds a constant, which dies out when the 'potential difference' is taken, dies in the gradient to solve for E. -- doesn't matter....
Yet naturally the potential at great distances should be zero as r goes to infinity.
we use this in solving problems, we will integrate in from infinity
note there is an issue with infinite sheets and lines ( but that isn't real world anyway)
It obeys superposition (just add them up)
Poisson's and Laplace's Equations
From Gauss's law
and
Nature of E field
Poisson's Equation
if there was no charge then
Laplace's Equation
save for later.
From Charge distributions
note, the r hat is gone,

and just over displacement magnitude
lines and surfaces are great too.
All related!!!
Boundaries
perpendicular part of E is off by across the boundary
parallel parts are the same.
Potential is also the same across a boundary

(gradient of potential is the same as perpendicular part of E)
Practice problem.
We can look at the source as well
Review (PH 220)
is path independent
more general, better!
Find V above a disk radius R charge density sigma, on axis of disk.
Find V inside a uniformly sphere radius R charge q.
try with both methods:
from E
from rho
aside
We will need these later, sorry we didn't prove them more, book does a great job.
The last question on the quiz said what doesn't remain constant across the boundary conditions of a charged surface.... The answer was the perpendicular component of E. Can you please explain????

Can we go over what potential is? I had a hard time understanding it even with how much it was covered in the chapter

I did not understand the concept behind the big O thing. Could you explain that ?

Can you explain the relationship between Electric field and Potential?
Full transcript