Final answer:
The electric field is the vector norm of the gradient of the electric potential. The electric potential is a scalar quantity that represents the electric potential energy per unit charge at a given point in space. The gradient of the electric potential represents the direction and magnitude of the electric field at any point in space.
Step-by-step explanation:
The electric field is the vector norm of the gradient of the electric potential. The electric potential is a scalar quantity that represents the electric potential energy per unit charge at a given point in space. On the other hand, the electric field is a vector quantity that represents the force per unit charge experienced by a test charge placed at a given point in space.
The gradient of a scalar field is a vector that points in the direction of the steepest increase of the scalar field. In this case, the gradient of the electric potential represents the direction and magnitude of the electric field at any point in space. Therefore, the electric field is calculated by taking the gradient of the electric potential and finding its vector norm.
For example, if the electric potential is given by V = kQ/r, where V is the electric potential, k is a constant, Q is the charge, and r is the distance from the point charge, the electric field can be calculated by taking the gradient of V and finding its vector norm.