Introduction:
In the study of electromagnetism, the relationship between the electric potential and electric field is a fundamental concept. The integral form of this relationship is given by a line integral.

Explanation:
- The electric potential, denoted by V, represents the amount of work done in bringing a unit positive charge from infinity to a particular point in the electric field. It is a scalar quantity and is measured in volts (V).
- The electric field, denoted by E, represents the force experienced by a unit positive charge placed at a particular point in the electric field. It is a vector quantity and is measured in volts per meter (V/m).

Line Integral:
- A line integral is a mathematical tool used to calculate the integral of a function along a curve or path.
- In the context of electromagnetism, the line integral is used to relate the electric potential and electric field along a specific path.
- The integral form of the potential and field relation is expressed as:

∫ E · dl = -∆V

where ∫ represents the line integral, E represents the electric field vector, dl represents an infinitesimal displacement vector along the path, and ∆V represents the change in electric potential.

Significance:
- The line integral of the electric field along a closed loop is zero, known as the conservative property of the electric field.
- This property allows us to define a scalar potential function V such that the electric field is the negative gradient of the potential, i.e., E = -∇V.
- By integrating the electric field vector along a specific path, we can determine the change in electric potential between two points.

Conclusion:
In conclusion, the integral form of the potential and field relation is given by a line integral. This mathematical tool allows us to calculate the change in electric potential along a specific path in the electric field. The relationship between the electric potential and electric field is crucial in understanding and analyzing various electrical phenomena.