Question

In which pictured region (if any) in the diagram above could the electric potential possibly be zero(excluding points at infinite distance from the spheres)?
The diagram shows two spheres, charged uniformly as indicated. All regions are along a line connecting the centers of the objects.
Region A is anywhere to the left of the 5.0 Coulomb charge. Region B is to the right of the 5.0 Coulomb charge and closer to the 5.0 Coulomb charge than to the 3.0 Coulomb charge. Region C is to the right of the 5.0 Coulomb charge but closer to the 3.0 Coulomb charge than to the 5.0 Coulomb charge. Region D is anywhere to the right of the 3.0 Coulomb charge.

• A. A
• B. B
• C. C
• D. D
• E. There is no region where the electric potential could possibly be zero.

Answer 1

Answer: (E)

There is no region where the electric potential could possibly be zero.

The equation for the electric potential surrounding a point charge (or a spherical object with uniform charge distribution) is:

$V=k\frac{q}{r}$

In this equation, $k$ is the Coulomb constant, $q$ is the amount of charge, and $r$ is the distance from the point charge to the location where we want to know the electric potential (or the distance from the center of the sphere to the location where we want to know the electric potential).

Electric potential is NOT a vector quantity, but can be positive or negative.

The only way we could possibly have a zero potential as a result of two charged objects is if we had one positively charged object and one negatively charged object.

In this case, both objects are positively charged, leading to a positive potential everywhere, except at an infinite distance from the objects

so the correct answer is option "E"