Problem 1
There are many ways to approach and do this problem. I’m going to present
what I think is the most straightforward way here.
We want to ultimately find a velocity, and the easiest way to do this is through
conservation of energy, which means we need to find the work done by the field,
which means we just need to find the
potential difference
between the two points.
Since we have a continuous charge distribution, we need to do an integral to
find
φ
, the potential [some people use
V
, which is just a matter of preference.]
The template integral for potentials is
Δ
φ
=
dq
4
π
0
r
So, we need to find
dq
,
r
, and appropriate limits. Let’s say that the charge is a
distance
D
away from the line of charge, and place our origin of coordinates at
the right end of the line and integrate to the left [there are many other choices
of origins and directions of integration that are all equivalent]. Then, the point
charge is at a distance
D
to the right of the origin, and the integration variable
will be
x
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 Spring '08
 Packard
 Charge, Electric charge, Fundamental physics concepts, charge density, Rser

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