Potential Energy External Field

Work is collected and stored as potential energy in the body when an external force is used to conduct work, such as moving a body from one point to another against a force like spring force or gravitational force. The body moves when an external force is removed, gaining kinetic energy while losing potential energy in equal quantities. The whole kinetic and potential energy is thus conserved. Conservative forces are included in this category. Instances of these forces are spring force and gravitational force.

Potential energy

As a function of its position, an object can store energy. When a destruction machine’s heavy ball is maintained at an elevated position, for example, it stores energy. Potential energy is the name given to this stored positional energy. A drawn bow, likewise, can store energy as a result of its position. There is no energy stored in the bow when it is in its normal position (i.e., when it is not drawn). The bow, on the other hand, can store energy when its position is changed from its normal equilibrium state. Potential energy is the name given to this stored positional energy. 

Gravitational potential energy

The energy held in an object due to its vertical position or height is known as gravitational potential energy. The gravitational pull of the earth to the object stores the energy. The mass of a demolition machine’s enormous ball and the height to which it is raised determine its gravitational potential energy. The gravitational potential energy of an object is proportional to its mass. Gravitational potential energy is higher in more massive objects. Similarly, an object’s gravitational potential energy is related to its height. The gravitational potential energy of an object increases as it is raised in elevation. The formula of gravitational potential energy is given as :

 PEgrav=mass ×gravity ×height

Elastic potential energy examples

We’ll talk about elastic potential energy as the second type of potential energy. The energy held in elastic materials as a result of stretching or compressing is known as elastic potential energy. Rubber bands, bungee chords, trampolines, springs, an arrow drawn into a bow, and other elastic potential energy storage devices exist. The quantity of elastic potential energy stored in such a device is proportional to its stretch; the greater the stretch, the more energy is stored.

Springs are a type of device that may store elastomeric potential energy through compression or stretching. Compressing a spring necessitates a force; the more compression there is, the more force is required to compress it further.

The amount of force applied to some springs is directly proportional to the degree of stretch or compression (x); this proportionality constant is referred as the spring constant k.

 Fspring=k×x

Potential energy external field

The potential energy of a single charge:

From one point to another point, the external electric field E and the related external potential V may differ. V at a point P is defined as the work required to deliver a unit positive charge from infinity to the point P.

qV is the amount of work required to bring a charge q from infinity to point P in the external field. The potential energy of q is used to store this work. If the position vector r of the point P is relative to some origin,

 Potential energy of q at r in an external field=qV(r)

How to derive potential energy

By virtue of its motion, an item possesses potential energy. Let’s say the body’s mass is m and it’s hoisted to h metres above the earth. It’ll get the job done. We all understand that work is measured in terms of force and displacement.

In this situation, the body’s distance is h, and the work done is given by:

 W=F×h …. (1)

Under the influence of gravity, the body moves higher. The object is being acted upon by gravity, i.e. F=mg

Now the equation 1 becomes:

 w=mg ×h

As we know work is taken as the form of energy so,

 E=mgh

Conclusion

The energy carried by a body as a result of its position or configuration is known as potential energy. It is also known as stored energy, and it aids in the completion of any task. The gravitational potential energy is the energy that an object has as a result of its position in relation to the ground. The energy related with the compression or expansion of an elastic spring is referred to as elastic potential energy. The thrilling roller coaster ride that we enjoy is likewise based on the potential energy idea. The ride is permitted to plummet from a height where potential energy can be converted to kinetic energy. Springs are a type of device that may store elastomeric potential energy through compression or stretching. The body moves when an external force is removed, gaining kinetic energy while losing potential energy in equal quantities.