Electric Field due to Continuous Charge Distributions

The electric field at a point P due to each charge element dq is given by Coulomb's law

where r is the distance from dq to P and is the corresponding unit vector. Here, dq = dV or dA or dl depending on charge distribution. Using the superposition principle, the total electric field is the vector sum (integral) of all these infinitesimal contributions

Note: This is an example of a vector integral which consists of three separate integrations, one for each component of the electric field.