The electric field (E) is defined as the negative gradient of the electric potential (V), represented mathematically as E_{x}=-\frac{\partial V}{\partial x}, E_{y}=-\frac{\partial V}{\partial y}, and E_{z}=-\frac{\partial V}{\partial z}. This indicates that each component of the electric field corresponds to the negative derivative of the electric potential with respect to its respective spatial coordinate. The relationship is indeed valid, confirming that E is the negative derivative of V in a vector form.
PREREQUISITESStudents of physics, particularly those studying electromagnetism, as well as educators and anyone seeking to deepen their understanding of the relationship between electric fields and electric potential.
kuruman said:You need to sharpen your thinking. The electric field is a vector, so to specify it you need to specify its three components. These are
E_{x}=-\frac{\partial V}{\partial x}; E_{y}=-\frac{\partial V}{\partial y};E_{z}=-\frac{\partial V}{\partial z}