Relation between Electric Field and Electric Potential:
Electric field and electric potential are closely related concepts in the field of electromagnetism. The relationship between the two can be understood through mathematical expressions and principles.

Gauss's Law:
One of the fundamental equations in electromagnetism is Gauss's Law, which states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space. Mathematically, this can be expressed as:
Φ = q / ε₀
where Φ is the electric flux, q is the charge enclosed, and ε₀ is the permittivity of free space.

Relation between Electric Field and Electric Potential:
The electric field (E) at a point in space is defined as the force per unit charge experienced by a test charge placed at that point. Mathematically, it is given by:
E = -∇V
where V is the electric potential at that point. This expression shows that the electric field is the negative gradient of the electric potential. In other words, the electric field points in the direction of the steepest decrease in the electric potential.

Relationship in Differential Form:
In differential form, the relationship between electric field and electric potential can be expressed as:
E = -dV/dr
where dV is the change in electric potential with respect to distance (dr). This equation shows how the electric field is related to the rate of change of electric potential in a given direction.