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P16 PH 333 2.3.1-2.3.5
Transcript of P16 PH 333 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
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
Nature of E field
if there was no charge then
save for later.
From Charge distributions
note, the r hat is gone,
and just over displacement magnitude
lines and surfaces are great too.
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)
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:
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?