The relationship between electric field (E) and electric potential (V) is defined by the equations E=keQ/r² and V=keQ/r. The electric field represents force per unit charge, while electric potential indicates energy per unit charge. The inverse square relationship in the electric field (1/r²) arises from the derivative of the potential (1/r), as E is the negative gradient of V, expressed mathematically as E = -∇V. This connection clarifies how the electric field diminishes with distance squared, while potential decreases linearly with distance.
PREREQUISITESPhysics students, electrical engineers, and anyone interested in understanding the fundamental principles of electromagnetism and the mathematical relationships between electric fields and potentials.
spencerthought said:E=keQ/r2 and V=keQ/r , I'm curious as to what what causes the relationship to r vs r2. I know the electric field is a measure of force per unit charge and the electric potential is a measure of energy per unit charge, just struggling to mentally connect where the inverse square relation to distance loses the square.