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

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Answer 1 · 2017-09-03T15:11:37

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

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

F = -#G.(m_1 m_2)/r^2# (this is the only one you need to recall)

Because energy = force x distance,

#E_g = -G. (m_1 m_2)/r #

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

#V_g = -G. (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. (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:

enter image source here