What is the relationship between electric potential and the electric field?

[lampshader]

I know of the equations can be found here: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/engfie.html


And the equations are similar both involving permittivity, but I don't know their fudemental relationship.

Could someone help? Thanks in advance.

 

[rootX]

?

 

[Andy Resnick]

The electric field is the gradient of the electric potential.

 

[torquil]

The electric field is the gradient of the electric potential.

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

Torquil