Question

Find the following limits. If the limit is undefined, identify whether it's +[infinity] or -[infinity]. If L'Hopital's rule is applied, state it.

Answer 1

To find the limit of the potential of a finite uniformly charged rod, we can use the formula for the potential of a point charge. By considering each element of the rod as a point charge, we can integrate the potential contributions from each element to find the total potential of the rod. This limit coincides with the formula for the potential of a point charge because as the length of the rod approaches infinity, the distance from any point on the rod to the observation point becomes effectively the same as the distance from the point charge to the observation point.

Step-by-step explanation:

In order to find the limit of the potential of a finite uniformly charged rod, we can use the formula for the potential of a point charge. The formula for the potential of a point charge is given by V = k(Q/r), where V is the potential, k is the electrostatic constant, Q is the charge, and r is the distance from the charge. By considering each element of the rod as a point charge, we can integrate the potential contributions from each element to find the total potential of the rod. This limit coincides with the formula for the potential of a point charge because as the length of the rod approaches infinity, the distance from any point on the rod to the observation point becomes effectively the same as the distance from the point charge to the observation point.