Question

what is the relation between electric field intensity and electric potential also say formula for solving partial derivatives and partial integration​

Answer 1

What is the relation between electric potential and electric field?

Electric field can exist only if there is a difference in potential. Potential, however high, if it is equal at all points, there will be no electric field. This is what happens inside a charged hollow sphere. Inside the sphere, there is potential, but no potential difference, hence no field.

Thus, in general Electric field is defined as negative space derivative of potential.

Considering one dimensional case for simplicity,

E = - dV/dx

Or E= - (gradient of potential)

(-) sign indicates that field is directed from higher potential to lower potential.