Potential at a Point: A Question of Solutions

[Guillem_dlc]

Homework Statement

If the electric field created by a one-point charge system is zero:
a) The potential at this point is always negative.
b) The potential at this point can be of any value.
c) The potential at this point is always positive.
d) The potential at this point is zero.

Relevant Equations

Potential and electric field

I thought the right choice was d). But when it comes to the solutions, it is b) and I don't understand why.

My reasoning would be: the potential at a point is the work that the electric field does to transport a charge from infinity to that point, so if the field is zero, it does no work and therefore the potential at that point is also zero.

 

[TSny]

Homework Statement:: If the electric field created by a one-point charge system is zero:

This part of the problem statement is worded a little oddly to me. I think that it probably meant to say something like, "If the electric field created by a system of charges is zero at a certain point: "

So, I don't think it's saying that the electric field is zero everywhere. The field just happens to be zero at a specific point. Then you want to consider the value of the potential at that point.

 

[Orodruin]

As to why (b) is correct: You can never tell the potential from the field at a single point. The field will only tell you about the derivative of the potential, not its value.