A conducting sphere of radius R carries an excess positive charge and is very far from any other charges.Which one of the following graphs best illustrates the potential (relative to infinity)produced by this sphere as a function of the distance r from the center of the sphere?

Question

Quizplus · Accepted Answer

For a conducting sphere carrying excess charge, the potential (relative to infinity) is given by V(r)=kQ/r, where k is the Coulomb constant, Q is the amount of charge on the sphere, and r is the distance from the center of the sphere. 
As we move away from the sphere, the potential should decrease inversely proportional to the distance. Therefore, the graph that best represents this relationship is the one that decreases sharply at first and then levels off to a small, finite value. 
Option D is the only one that satisfies this condition.

A Conducting Sphere of Radius R Carries an Excess Positive