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Electric field and its work on charges
We introduced the concept of electric field and this formula:
F
=
q
·
E
What can you associate force with?
Motion or acceleration from
F
= m
a
.
Work, from W =
F
·
X
(a review on vector dot product here).
Example with a uniform electric field:
E
X
Y
A
B
C
D
The work to the field E does to move the charge from A to B is:
W
AB
=
F
·AB =
q
E
·
X
=
q
EX,
where
X
is the vector from A to B.
From A to D:
W
AD
=
F
·AD =
q
E
·
Y
=
q
EX = W
AB
,
where
Y
is the vector from A to D. And this
answer is true no matter the path is ABD, ACD or AD.
So the electric force
F
=
q
E
is conservative.
(a review on conservative force).
q
X
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Electric Potential
Electric potential of an electric field.
Electric field exerts force on a charge inside it.
This force moves the charge and does work to it. The work the electric
force does not depend on the path, but only the start and end points of
the charge
the electric force is conservative.
For a charge in a conservative force field, one can define a potential that
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 Spring '08
 Ye
 Charge, Magnetism, Acceleration, Force, Work, Electric charge

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