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A convenient choice of reference that relies on our common sense is that when the two charges are infinitely far apart, there is no interaction between them. (Recall the discussion of reference potential energy in Potential Energy and Conservation of Energy .) Taking the potential energy of this state to be zero removes the term from the equation (just like when we say the ground is zero potential energy in a gravitational potential energy problem), and the potential energy of Q when it is separated from q by a distance r assumes the form
This formula is symmetrical with respect to q and Q , so it is best described as the potential energy of the two-charge system.
What is the change in the potential energy of the two-charge system from to
Check Your Understanding What is the potential energy of Q relative to the zero reference at infinity at in the above example?
It has kinetic energy of at point and potential energy of which means that as Q approaches infinity, its kinetic energy totals three times the kinetic energy at since all of the potential energy gets converted to kinetic.
Due to Coulomb’s law, the forces due to multiple charges on a test charge Q superimpose; they may be calculated individually and then added. This implies that the work integrals and hence the resulting potential energies exhibit the same behavior. To demonstrate this, we consider an example of assembling a system of four charges.
Step 2. While keeping the charge fixed at the origin, bring the charge to ( [link] ). Now, the applied force must do work against the force exerted by the charge fixed at the origin. The work done equals the change in the potential energy of the charge:
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