When is electric field zero and electric potential non zero

[mrcotton]

Homework Statement

Which one of the following statements about electric field strength and electric potential is
incorrect?
A Electric potential is a scalar quantity.
B Electric field strength is a vector quantity.
C Electric potential is zero whenever the electric field strength is zero.
D The potential gradient is proportional to the electric field strength.

Homework Equations

E=K Q/(R^2)
V=K Q/R

K=1/(4∏ε)

The Attempt at a Solution

The answer is C

If for example you had two positive charges of 3 coulombs a distance 4m apart.
The electrostatic field at the midpoint would be zero. Effectively a positive charge at this point would be push by an equal force in both directions.

However the Electric potential V would be 2*(k*(3/4)

So you can have a zero E with a non zero V

Is this logic ok
Thanks for any help

 

[CAF123]

However the Electric potential V would be 2*(k*(3/4)

So you can have a zero E with a non zero V

Is this logic ok
Thanks for any help

The electrical potential goes as 1/r, but your reasoning is correct. You could also consider the electric potential and electric fields associated with spherical conductors: Provided the conductor is closed, the E field inside is 0 but the potential is a constant.