3. Aositive and a negative point charge of absolute value q are a distance d awa
ID: 1769844 • Letter: 3
Question
3. Aositive and a negative point charge of absolute value q are a distance d away, as shown at right. a. With the two charges infinitely far apart as a reference configuration, is the -q electrostatic potential energy of the system positive, negative, or zero? Explain based on the work energy theorem: WextAK + AU b. Consider calculating the electrostatic potential energy from u: 2 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 her, where V other is the potential due to the charge(s) other than the d. c. Is it possible to use superposition to find the electrostatic potential energy of this configuration with this method? Explain i. ii. 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? 6. 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 choose to put the reference point arywhere. Doesn't that mean that the potential at a point is undefined?"Explanation / Answer
a (i) The two charges are of the same magnitude and are not in motion, so the total energy of the system will be equal to the potential energy, which is negative in nature as it represents the work done against the force. So work done will be negative.
b (i) Electropotential energy is a scalar quantity and thus it always follows superposition principle according to which the total potential energy is a sum of potential energies on the individual charges.
(ii) Potential will be same throughout t so we don't need to consider the whole space along which the electric field is acting.
c (i) Here, the potential energy is not representing linear characteristics so superposition principle is not valid for this case,
(ii) Since superposition principle is not applicable we have to calculate the potential energy at different points and thus have to calculate for all space.
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