Thanks, and no I havent.blue_leaf77 said: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?
An electric field is a physical field that surrounds any electrically charged object. It exerts a force on other charged objects within its range, causing them to either attract or repel from each other.
This equation, known as the gradient of potential, is used to calculate the strength and direction of the electric field at a given point in space. It relates the electric field (E) to the potential (V) at that point.
The symbol ∇ (nabla) represents the gradient operator, which is a mathematical tool used to find the rate of change of a function in multiple dimensions. In this case, it is used to find the change in potential (V) with respect to position.
This equation is known as the Maxwell-Faraday equation and is one of the four Maxwell's equations that describe the behavior of electromagnetic fields. It relates the electric field (E) to the time rate of change of the vector potential (A), which is a quantity used to describe the magnetic field in electromagnetic waves.
The negative sign indicates that the electric field points in the direction of decreasing potential. In other words, it shows that the electric field will always try to move a charged particle towards regions of lower potential.