Relationship between Electric Field and Potentential

[spencerthought]

E=k_eQ/r² and V=k_eQ/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.

 

[rumborak]

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

 

[ZapperZ]

E=k_eQ/r² and V=k_eQ/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.