Finding the relationship between electric potential and the electric field

lampshader

1. The problem statement, all variables and given/known data

Consider if these things are scalars or vectors. Which is easier to work with, scalar or vector quantities? What is the relationship between electric potential and the electric field?

2. Relevant equations
The electric field equation:
E = 4*pi*k*sigma / (- (base zero)
The electric potential equation:
/\U (base E) = -W(base E) = -q*E*d


3. The attempt at a solution

Scalar values are easier to work because they are just simple values. With vectors it is can be problematic for the reason that vectors have both a value and a direction.

I think that the relationship between electric feild and potential can be described by the following equation:
C = 1 / sqrt( u(base 0) * permittivity (base 0) )

The electric field is the gradient of electric potential. However, if there is a time-varying magnetic field present, the electric field is not fully described by the electric potential. The electric field has a contribution from the time-derivative of the magnetic vector potential.