# What is the relationship between force and potenial energy in fields?

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Forces are what allows potential energy to occur. The force that is associated with potential energy is called gravitational force. Gravitational force is a force that pull objects downward. In terms of potential energy, gravitational is what holds an object in place. For example, you were a ball sitting on top of the hill. The ball on top of the hill has potential energy because it's not moving on top of the hill. The force that is holding the ball on top of the hill is called gravitational force because gravity is allowing the ball to keep its position. The formulas to represent this relationship is shown below:

The gravitational potential energy is given:

PE(grav) = mass object x gravitational field (9.8m/s) x height of object

As the mass and height increases, the force increases and vice versa.

Under gravitational field force acting on a body of mass **m **is given as:

F=GMm/R^2 ------------(1)

In this field,pontial energy of the body is given as:

PE=-GMm/R----------------(2)

Dividing eq.(1) by eq.(2)

- F/PE =1/R

=>

F=-PE/R