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Four point charges form a square with sides of length
, as shown in the figure. In the questions that
follow, use the constant
in place of
.
Part A
What is the electric potential
at the center of the square?
Make the usual assumption that the potential tends to zero far away from a charge.
Hint A.1
How to approach the problem
Hint not displayed
Hint A.2
Find the distance to the center
Hint not displayed

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Part A
Express your answer in terms of
,
, and appropriate constants.
ANSWER:
=
Correct
Part B
What is the contribution
to the electric potential
energy
of the system, due to interactions
involving the charge
?
Hint B.1
Hint not displayed
Express your answer in terms of
,
, and appropriate constants.
ANSWER:
=
Correct

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Part C
What is the total electric potential energy
of this system of charges?
Hint C.1
How to approach the problem
Hint not displayed
Hint C.2
How many pairs?
Hint not displayed
Express your answer in terms of
,
, and appropriate constants.
ANSWER:
=
Correct
Imagine now that charge
is released, and it drifts away from the rest of the charges, which remain
fixed in place.
Part D
What would be the kinetic energy
of charge
at a very large distance from the other charges?
Hint D.1
What happens to energy?
Hint not displayed

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Part D
Express your answer in terms of
,
, and appropriate constants.
ANSWER:
=
Correct
It should not come as a surprise that the answer to Part D is equal to the intial contribution to the
potential energy of the system due to the presence of charge
. Initially, the
kinetic energy
of
charge
is zero. Because the electric potential between two charges is inversely proportional to the
distance between them, after charge
has drifted far away from the others,
(see B) is (very
close to) zero. Since total energy is conserved, the change in potential energy must have been
converted into kinetic energy.
Part E
What will be the potential energy
of the system of charges when charge
is at a very large
distance from the other charges?
Hint E.1
Hint not displayed

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Part D
Express your answer in terms of
,
, and appropriate constants.
ANSWER:
=
Correct
There are two ways you could have approached this question. You could have found the sum of the
three terms corresponding to the three remaining pairs of charges, or you could have subtracted the
initial
from the total energy of the system before charge
was removed.

Electric Potential Ranking Task
In the figure
there are
two point charges,
and
. There are also six positions, labeled A through F, at various
distances from the two point charges. You will be asked about the electric potential at the different
points (A through F).
Part A

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