A positive and a negative point charge of absolute value q are a distance d away
ID: 1791300 • Letter: A
Question
A positive and a negative point charge of absolute value q are a distance d away, as shown at right. +4 With the two charges infinitely far apart as a reference configuration, is the electrostatic potential energy of the system positive, negative, or zero? Explain based on the work energy theorem: Wext-AK + U. a. b. Consider calculating the electrostatic potential energy from uE = 2E0E" Is it possible to use superposition to find the electrostatic potential energy of this configuration with this method? Explain. (Hint: Is the energy density linear in charge?) i. In general, if the charge distribution is localized in one region of space, is your sum or integral bounded by where the charges are, or do you still have to consider all space? ii. Consider calculating the electrostatic potential energy from dUE =-dqV other, where Voter is the potential due to the charge(s) other than the da. c. Is it possible to use superposition to find the electrostatic potential energy of this configuration with this method? Explain. i. In general, if the charge distribution is localized in one region of space, is your sum or integral bounded by where the charges are, or do you still have to consider all space? ii. Three students discuss the potential of a single point charge. How would you answer the questions raised by each student? Explain your reasoning. Student 1: "The potential at a point depends on what the reference point is, and we can ch to put the reference point anywhere. Doesn't that mean that the potential at a point is undefined?"Explanation / Answer
(a)
As d goes to infinity, the electrostatic potential energy becomes zero.
(b)
(i)
As energy density is not linear in charge(see the dependence of energy density on E), it's not possible with the superposition.
(ii)
Yes, we have to consider all space as the charge may be localized in a region but the electric field may be nonzero outside that region. So, we have to consider all space.
(c)
(i)
It is possible with this method as V is a linear function of q.
(ii)
Q1.
Yes, the potential at a point is undefined as potential can always be written as the sum of two terms where one of the terms comes due to our choice of the reference point. At a given point we can have different values of the potential for different choices of reference points unless we are stuck to a particular reference point.
Q2.
It's just like saying that we can put origin at every point in space so that every point has the same coordinate. There is nothing wrong in doing so but it won't make any practical sense. So we have to stick to a reference point (In this case infinity).
Q3.
Yes, the potential at a point can never be zero unless its infinitely far away.
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