Question

Define potential energy. Obtain the expression for potential energy.

Answer 1

Potential energy is a form of energy that a body possesses due to its position, you can use the gravitational potential energy as an example. The potential energy of a body is given by the general equation ${E_P} = Force \times Displacement$ and this equation can be modified as per the given system (the equation becomes ${E_P} = mgh$ for objects in earth’s gravitational field and ${E_P} = K\dfrac{{Qq}}{r}$ in case of charge in electric fields and so on).

Complete answer:
Potential energy refers to the energy that a body possesses due to its position in a system.
Energy refers to the ability to do work, to understand potential energy more clearly let’s take the example of a ball. When the ball is lying on the ground it does not have any potential energy and hence the ball cannot do any work. When we raise the ball to a certain height from the surface the body gains some potential energy. Now how do we know that the ball lifted to a certain height has some potential energy, this is because if we leave the ball at that height the ball will begin to fall towards the surface. This process of going down is the work done by the ball and the ball gains the ability to do this work when we provide it with potential energy by raising it.
The example used above demonstrates how an object in a gravitational field possesses potential energy, similarly charges in an electrostatic field, magnetic objects in a magnetic field, stretched spring, etc. also possess potential energy.
The general expression of potential energy in any system is
${E_P} = Force \times Displacement$
So, for a body to possess potential energy it should be displaced against a force in a system.
In the example used above gravitational pull on the ball was the force which would have opposed the lifting of the ball. So, for the example
$Force = mg$
Here, $m =$ the mass of the body and $g =$ the acceleration due to gravity
$Displacement = Height = h$
${E_P} = mgh$
If we consider a charge in the electric field, we have
$Force = K\dfrac{{Qq}}{{{r^2}}}$
Here, $K =$ Proportionality constant
$Q =$ The magnitude of charge that produces the electric field
$q =$ The magnitude of the charge for which potential energy is to be calculated
$r =$ Distance between the two charges
$Displacement = r$
So, ${E_P} = K\dfrac{{Qq}}{{{r^2}}} \times r = K\dfrac{{Qq}}{r}$
You can use the expression for the potential energy of a body in any system by using the general equation of potential energy, i.e. ${E_P} = Force \times Displacement$ .

Note:
Under ideal conditions the potential energy in any system will only depend on the initial and the final position of the object, for example, a spring extended to a certain length $x$ will always have the same potential energy, i.e. ${E_P} = Fx$, no matter if you had compressed or stretched it first.