Electric Potential Energy — Question 2

Question 2

Three work measurements can expose an inconsistent electrostatic claim

For the same fixed test charge in a static field, measured electric works are $W_{A\to B}=8.00\,\mu$J and $W_{B\to C}=-3.00\,\mu$J. A third report claims $W_{A\to C}=6.00\,\mu$J. Treat all values as exact.

1. Use potential-energy differences to predict the third work.

2. Calculate the closed-loop work implied by the three reports and identify the required correction if the first two are retained.

Question 2 - Solution

Three work measurements can expose an inconsistent electrostatic claim

(a) Method and calculation

$$U_B-U_A=-8.00\,\mu\mathrm J,\quad U_C-U_B=+3.00\,\mu\mathrm J.$$$$U_C-U_A=-5.00\,\mu\mathrm J\Rightarrow W_{A\to C}=+5.00\,\mu\mathrm J.$$

(b) Interpretation and further calculation

$$W_{A\to B\to C\to A}=8.00-3.00-6.00=-1.00\,\mu\mathrm J\ne0.$$$$W_{A\to C}:\quad6.00\longrightarrow5.00\,\mu\mathrm J.$$The exact reports cannot all describe the same conservative electrostatic field.

Physical check

Any path-dependent mechanical losses must be separated from electric work before testing conservativeness.