Question

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

Answer 1

Answer:

See annex

Explanation:

By convention potential at ∞    V(∞ ) = 0

As the distance from the sphere decreases the potential increases up to the point d = R  ( R is the radius of the sphere. That potential remains constant while d = R and becomes 0 inside the sphere where there is not free charges and therefore the electric field is 0 and so is the potential.

I am sorry I could not make a better graph

Answer 2

The graph that best  illustrates the potential (relative to infinity) produced by this sphere as a function of the distance r from the center of the sphere is attached as an image below

$V = \frac{KQ}{R}$

for r <= R

$V = \frac{KQ}{r}$

for  r > R  

Therefore the graph will be

For more information on potentials as function of distance

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