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Electric potential energy of a system of charges

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The electric potential energy of a system of point charges is defined as the required assembling this system of charges by bringing them close together, as in the system from an distance

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Simple case of two charges q1 and q2

We consider the charges q1 and q2 initially at infinity

Suppose, first the charge q1 is brought from infinity to the point r1. work done in bringing q1 from infinity to r1 is

Then work done in bringing charge q2 from infinity to the point r2 is proportional to q1q2 and inversely proportional to

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Like and Unlike charges

Question 1

If q1 q2 > 0, potential energy is positive

Question 2

For unlike charges (q1 q2 < 0), the electrostatic force is attractive, and the Potential energy is positive

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