Finding the relationship between electric potential and the electric field

[lampshader]

Homework Statement

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?

Homework 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

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 field 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.

 

[anathema]

This is known as the "magnetic vector potential contribution" or "magnetic vector potential term." This can be seen in the equation for the electric field:

E = -∇V - ∂A/∂t

Where V is the electric potential and A is the magnetic vector potential. This relationship shows that the electric field is dependent on both the electric potential and the magnetic vector potential.

Furthermore, the electric potential and the electric field have a direct relationship. The electric potential is the work done per unit charge to move a charge from one point to another in an electric field. This can be seen in the equation:

V = W/q

Where V is the electric potential, W is the work done, and q is the charge. Therefore, the electric potential is directly related to the electric field, as the electric field is what causes the work to be done.