Problem 3: An energy conundrum There is a bit of a conundrum that occurs when we...

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Problem 3: An energy conundrum There is a bit of a conundrum that occurs when we begin to compare our two different descriptions of energy associated with electrostatic systems. Consider two point charges q and 92 that are a distance d apart. You can locate them anywhere to develop this argument, but for the sake of clarity, let's put them on the x-axis, one at the origin and the other at x = d. (a) Compute the work done to bring the charge configuration together. Recall that it costs nothing (i.e., there is no work done) to bring the first charge to its location. Does this expression look familiar? (b) Now write down the total energy associated with the charge configuration using the integral formula: Edr. Remember that the electric field in this integral expression is due to the field from both charges: E = E + E2. Do not try to integrate it. (c) Your integral expression can be expanded out to three terms. In principle, you can integrate one of the terms, but not the other two. Which two are not integrable and why not? What is the physical significance of the two non-integrable terms? Compute the integrable term. Problem 3: An energy conundrum There is a bit of a conundrum that occurs when we begin to compare our two different descriptions of energy associated with electrostatic systems. Consider two point charges q and 92 that are a distance d apart. You can locate them anywhere to develop this argument, but for the sake of clarity, let's put them on the x-axis, one at the origin and the other at x = d. (a) Compute the work done to bring the charge configuration together. Recall that it costs nothing (i.e., there is no work done) to bring the first charge to its location. Does this expression look familiar? (b) Now write down the total energy associated with the charge configuration using the integral formula: Edr. Remember that the electric field in this integral expression is due to the field from both charges: E = E + E2. Do not try to integrate it. (c) Your integral expression can be expanded out to three terms. In principle, you can integrate one of the terms, but not the other two. Which two are not integrable and why not? What is the physical significance of the two non-integrable terms? Compute the integrable term.