Electric Field Confusion: Explaining E=-∇V & E=-∇V-∂A/∂t

[Isaac0427]

Hi all! I know that this might be a stupid question, but I am very confused about a particular aspect of the electric field. I have seen these equations:
E=-∇V and E=-∇V-∂A/∂t
Could you guys explain how the electric field can be explained with or without -∂A/∂t

 

[blue_leaf77]

The first is for electrostatic case where the electric field is a conservative field (its curl vanishes), the second is in the case of electrodynamics where both electric and magnetic fields are changing with time. Have you taken EM course?

 

[Isaac0427]

The first is for electrostatic case where the electric field is a conservative field (its curl vanishes), the second is in the case of electrodynamics where both electric and magnetic fields are changing with time. Have you taken EM course?

Thanks, and no I havent.