# What is relation between the force acting on a particle and its potential energy? explain.

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Sep 3, 2017

This isn't simple, but I can show you a cool technique for only needing to recall a single equation and deriving the rest.

#### Explanation:

We'll take gravity as the simplest example, equivalent equations for electrical and magnetic fields just involve altering the constants.

F = -$G . \frac{{m}_{1} {m}_{2}}{r} ^ 2$ (this is the only one you need to recall)

Because energy = force x distance,

${E}_{g} = - G . \frac{{m}_{1} {m}_{2}}{r}$

Potential is defined as being energy per unit mass, so the equation will be:

${V}_{g} = - G . \frac{{m}_{1}}{r}$

and finally field strength is change in potential per unit distance (the gradient, or first derivative of the potential - distance curve)

$g = - G . \frac{{m}_{1}}{r} ^ 2$

Finally, as we know F = m.g, we get back to where we started by multiplying by mass.

Pretty nifty, eh?

Just to help, I've attached a photo that shows the symmetry of the cycle: