I am having trouble with the following question from Giancoli\'sPhysics for Scie

Question

I am having trouble with the following question from Giancoli'sPhysics for Scientists & Engineers, 4th ed, Chapter 23, Problem#36: "A total charge Q is uniformly distributed on athread of length l. The thread forms a semicircle. What is the potential at the center? (Assume V=0 atlarge distances.)"
Here is what I know so far: the length of the threadis r. Here is what I don't know: everything else. Ithink I am missing a fundamental concept because I don't reallyunderstand the significance of noting that V=0 at large distancesand I also don't really understand the difference betweencalculating the charge at a specific point (like the center of acircle) as opposed to the charge across a surface.
If anyone can share some insight about how to answer thisproblem, I would really appreciate it! Thanks!
"A total charge Q is uniformly distributed on athread of length l. The thread forms a semicircle. What is the potential at the center? (Assume V=0 atlarge distances.)"
Here is what I know so far: the length of the threadis r. Here is what I don't know: everything else. Ithink I am missing a fundamental concept because I don't reallyunderstand the significance of noting that V=0 at large distancesand I also don't really understand the difference betweencalculating the charge at a specific point (like the center of acircle) as opposed to the charge across a surface.
If anyone can share some insight about how to answer thisproblem, I would really appreciate it! Thanks!

Explanation / Answer

V = Q / (4 0 d)   definition of electric potential at a point at distance d fromQ This is the work done in bringing a unit positive test chargefrom infinity to the point being considered. If you bring the test charge in along the axis of thesemicircle one can see that it doesn't make any difference if Q is a single charge at distance R from the axis or anumber of charges distributed at distance R from the axis. The work woulde be the same in either case from symmetryconsiderations. R = L / V = Q / (4 0 L)

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