To calculate electric potential by integrating the electric field, you first need to determine the electric field at every point in space using Coulomb's law or Gauss's law. Then, you can use the formula V = -∫E•dl to integrate the electric field along a path from a reference point to the desired point. This will give you the electric potential at that point.
The electric field is the negative gradient of the electric potential, meaning that the electric field points in the direction of decreasing potential. In other words, the electric field is the force per unit charge experienced by a test charge in an electric field. This relationship is described by the equation E = -∇V.
Equipotential surfaces are imaginary surfaces in space where the electric potential is constant. This means that no work is required to move a test charge along an equipotential surface, as the potential does not change. The electric field is always perpendicular to an equipotential surface, and the closer the lines of electric field are to each other, the stronger the electric field is at that point.
Electric potential is a scalar quantity that describes the potential energy per unit charge at a particular point in space. On the other hand, electric potential energy is the potential energy of a system of charges due to their positions and charges. Electric potential is measured in volts, while electric potential energy is measured in joules.
One example of using this formula is to calculate the electric potential at a point between two parallel plates with opposite charges. First, you would find the electric field between the plates using Coulomb's law. Then, you can integrate the electric field along a path from one plate to the desired point to find the electric potential at that point. This can be useful in understanding the behavior of electric charges in a parallel plate capacitor.