Physics
The governing equations for electric fields are derived from Maxwell's equations and focus on the behavior of electric fields in the presence of charges and materials. These include Gauss's Law and the equation for the relationship between electric field and potential.
Gauss's Law for Electric Fields
Gauss's Law states that the electric flux through a closed surface is proportional to the enclosed electric charge. This equation forms the foundation for understanding how charges produce electric fields.
where,
• 
— Charge density 
— Charge density • 
— Electric field vector 
— Electric field vector • 
— Permittivity of the medium 
— Permittivity of the medium Relationship Between Electric Field and Electric Potential
The electric field is the negative gradient of the electric potential. This relationship provides a direct link between scalar potential and the vector field.
where,
• 
— Electric potential 
— Electric potential • — Electric field vector
— Electric field vector • 
— Gradient operator
— Gradient operator