In the figure below, a plastic rod having a uniformly distributed charge Q has b
ID: 1320458 • Letter: I
Question
In the figure below, a plastic rod having a uniformly distributed charge Q has been bent into a circular arc of radius R and central angle ?. With V = 0 at infinity, what is the electric potential at P, the center of curvature of the rod? State your answer in terms of the given variables, using ?0 if necessary.
I know it isn't
In the figure below, a plastic rod having a uniformly distributed charge Q has been bent into a circular arc of radius R and central angle ?. With V = 0 at infinity, what is the electric potential at P, the center of curvature of the rod? State your answer in terms of the given variables, using ?0 if necessaryExplanation / Answer
An arbitrary infinitesimal piece of the charge "dq" can be treated as a point charge and its potential "dV" at "P" is just;
dV = kdq/R
To get the total potential due to all the pieces (total charge) you just add them up. This requires integrating;
V = INTEGRAL[kdq/R]
In this problem "R" is the same for all dq's in the rod and is constant w.r.t to the integration so you can bring it out of the integral, along with k , to get;
V = (k/R)INTEGRAL[dq]
and this integration is just "Q" .So the final answer is simply;
V = kQ/R