# Relationship between Electric Field and Potentential

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.

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One is the derivative of the other. The derivative of 1/r gets you 1/r^2 (save some factor).

Fluxxx
ZapperZ
Staff Emeritus
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.
The most general form of the relationship between E and V is

$$E = -\nabla V$$

This means that E is the vector gradient of the potential field V.

Zz.

Fluxxx