Semicircular rod and Electric Potential Question

[kevtimc25]

Homework Statement

A thin, flexible rod of length L = 10 cm carries charge Q = 91 nC uniformly along its length. The rod is then bent into a semicircle, as shown in the figure. Show all work and circle answers. a) Find the electrical potential at the center.
b) Now we want to place a single point charge so that the electric potential is zero at the center. What are the coordinates of this charge’s positions (x,y) and what is the charge Q1 needed in Coulombs?

(I can't extract the figure, but its basically a semicircular rod of charge with a point where the center of the full circle would be.)

Homework Equations

U= kQq / r, λ = Q/L, C=2πr

The Attempt at a Solution

Part a.) We take (from 0-L)∫ dU = ∫(k/r)dQ => dQ = λdL, ∫(k/r)λdL => kλ/r * L ]from0-L
= (kλ/r) * L = kQ/r (same as U) , And we calculate r from 2L = 2πr.

But wouldn't the point charge in b) also be affected by the rod, and in that case we would have to vary 'r' as well to find that charge's elect. potential?

Much appreciated!

 

[Simon Bridge]

(a) looks like what I'd do.
(b) the potential at a point due to a charge does not depend on the presence of other charges... as your own equation shows.

 

[kevtimc25]

Got it, thanks!

 

[Simon Bridge]

... note: it would matter if the rod were a conductor, then it becomes quite a hard problem.
Fortunately you are told that the charge density is a constant - so it must be an insulator.