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carnot cycle
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Homework Statement
Two point charges are located on the x-axis, q1 = -e at x = 0 and q2=+e at x=a.(a)Find the work that must be done by an external force to bring a third point charge q3 = +e from infinity to x = 2a. (b) Find the total potential energy of the system of three charges.
The Attempt at a Solution
I am struggling with part a of this question
I found that the net force acting on q3 at x = 2a due to the charges q1 and q2 is the following:
F = 3Ke2/4a2
Where K is Coulomb's constant. This was done using Coulomb's law.
Now to find the work done by an external force in bringing the charge q3 from infinity to x = 2a, can't I just find the work done by the electric force in pushing the charge q3 from x = 2a to infinity? Should those two be equal in magnitude? If so, then I obtained the following answer after integration:
W = 3Ke2/(8a)
However, this answer is incorrect. The book states the following: W = 4Ke2/(8a). I am wondering where I went wrong. Thanks.