Final answer:
To find the limit L of the potential of a finite uniformly charged rod, we can use the ε−δ definition and integrate over the electric field and charge configuration of the rod. However, the limit does not exist due to the charges not being localized and extending to infinity.
Step-by-step explanation:
In this question, we are asked to find the limit L of the potential of a finite uniformly charged rod and prove that it coincides with the formula for a point charge. To do this, we can use the ε−δ definition and integrate over the electric field and charge configuration of the rod.
By taking the limit as the length of the rod goes to infinity, we can compare the potential to that of an infinite straight wire. However, this limit does not exist due to the charges not being localized and extending to infinity. This implies that our assumption of zero potential being an infinite distance from the wire is no longer valid.