# Can someone explain to me the difference between potential and potential energy in details?And,work done in a conservative force field is the difference in potential or potential energy?

Apr 18, 2018

Potential basically tells us the ability of an object to do some work .

And Potential energy is the amount of energy it acquires due to that Potential difference.

#### Explanation:

"NOTE" - Mostly we talk of Potential difference rather than Absolute Potential because it is a relative quantity.

Potential Energy is the energy which arises due to the difference in Potential.

Important observation :-

• Each object in the universe tries to attain low POTENTIAL state.
• That's why electric charges (+ve or -ve) move from region of high potential to low potential.
• Objects fall toward earth in the direction of decreasing POTENTIAL
• Electrons tend to be near the nucleus of the atom $i e$ in the region of least potential.

# Potential energy is a relative quantity, it depends on where we choose the potential energy to be Zero (Datum).

$$    This can be different in different respects for example :-

• Due to difference in vertical height , the Gravitational Potential changes and so does the Gravitational potential energy and this Gravitational potential energy is given by the formula :

• $P {E}_{g} = m g h$ ; where $m$ is the mass of the object ; $g$ is the acceleration due to gravity and $h$ is the height above the Datum line (which is the floor/ground normally). • The relation between the Force and Potential is :-
$\vec{F} = - \vec{\nabla} U$ where $F$ is the Force and $U$ is the potential.

• In case of a charged parallel plate Capacitor we can see that due to accumulated opposite charges on the plates ; a Potential difference is generated ; $i e$ it has ability to do some work and the amount of work it can do is known as the Potential Energy stored inside that capacitor. The answer is getting quite long, so I can't write more examples ; I hope it helps :)