AP Physics C — Arc of Charge

Find the Charge, The Electric Field, and Electric Potential Difference a distance away from the charged Arc.

Charge

We can use arclength and linear charge density .

Electric Field

Since the component of the electric field cancels out, we only need to look at the component using . In this problem, we also use found while looking for charge.

Electric Potential

All three solutions have to do with

1. splitting up the curved surface into small parts
2. replacing terms with charge density and other measures of length ().