# Can Potential energy be negative? [Explained with Reasons]

Potential energy is the energy possessed by the object due to its relative position, electric charge, elastic deformation, etc. But is it always remain positive?

Potential energies (P.E.) can be negative, positive, or zero, depending on the reference conditions. Negative gravitational P.E. means the object is below zero P.E. reference point. Negative electric P.E. means the work required to move oppositely charged particles apart against the electric field.

Read on to find out, Are different potential energies have a negative nature or not.

Contents:

## Can Gravitational potential energy be negative?

The positive and negative nature of the PE depends on the reference point.

If the object is raised at any height ‘h’ above the reference point, the object gains a positive P.E. and if the object is at a depth below the reference point, the object gains a negative P.E.

Typically, for gravitational PE, the reference point is considered at the earth’s surface. Thus it is considered that all objects on the ground have zero energy with respect to the earth’s surface.

As shown below figure, the water behind the dam has positive P.E. while the water in the deep well has negative P.E. and the bucket kept on the ground has zero P.E.

If the work against the gravitational field is necessary to bring the object closer to the reference point, then the object has a negative P.E. While if the work against the gravitational field is necessary to move away the object from the reference point, then the P.E. is positive.

Let me explain this with an example.

In the case of water in a deep well, you have to do work to bring the water on the ground i.e. on the reference point, thus the water in the well possesses negative P.E. As much the object moves away in the downward direction from the reference point, the negative P.E. of the object goes on increasing.

To move the water away from the ground (reference point) to the dam, work has to be done on the water. Thus with respect to the ground, the water in the dam possesses positive P.E. As much object goes up from the ground, the positive P.E. of the object goes on increasing.

## Can Electric potential energy be negative?

Electric potential energy is the energy required for the work of moving the charge against the electric field.

Negative electric P.E. is found between the oppositely charged particles while positive electric P.E. is found among the like charged particles (Both positive or both negative).

1] Negative electric potential energy:-

If the work is done against an electric field to separate away the particles, then the potential energy associated with it is negative electrical potential energy.

It happens in the case of opposite charges (Positive and negative). The opposite charges attract each other, thus to move these particles apart, the work has to be done against the electric field.

As much the opposite charges move apart, the charge particles get more negative potential energy.

2] Positive electric potential energy:-

If the work is done against an electric field in bringing the charges together, then the energy associated with it is positive potential energy.

It happens in case of like charges. The like charges repel each other, thus to bring these charges together, the work has to be done against the electric field.

As the charge particles come closer, their positive potential energy goes on increasing.

## Can Spring potential energy be negative?

The deflection in the spring (compression or elongation) causes potential energy to be stored in the spring.

It is given by,

\text{P.E.} = \frac{1){2}.(\text{Spring constant}).(\text{Deflection})^{2}

The spring’s potential energy is proportional to the square of the deflection in the spring. Therefore even if the deflection is negative, due to the squaring of the deflection, the potential energy always becomes positive.

The below graph represents the general idea for the variation of the potential energy based on the deflection.

It shows potential energy is zero at the unstretched condition and positive in both situations, during compression (-ve deflection) and expansion (+ve deflection).

Thus the potential energy of the spring remains positive irrespective of the direction of deflection in the spring.

## Can Change in potential energy be negative?

A change in potential energy indicates the difference between the initial potential energy and the final potential energy. If the initial PE is less than the final PE, then the change in PE becomes negative.

Consider an archer stretching bow from an unstretched condition. The unstretched bow has less PE than the stretched bow. Here, the potential energy of the bow is increasing and hence the change in potential energy becomes negative.

## Final words:

The intent behind this post is to understand what actually the negative potential energy means. It depends on the reference conditions used for the consideration.

But it is not possible for all types of potential energies. (e.g. Negative PE is not possible in the case of coil springs.)