# Electric potential energy

### Article about the Electric potential energy

Before studying this topic, first understand work, the conservative forces, the relationship between the conservative forces with potential energy, the electric forces and the electric field.

### Electric force is the conservative forces

In addition to the gravitational force and spring force, the other example of the conservative force is the electric force. To better understand why the electric force is called the conservative force, understand the following explanation. Suppose there are two electrically charged plates as shown in the figure, the left plate is positively charged, and the right plate is negatively charged. The arrow between the two plates is the electric field lines that come out of the positive charge towards the negative charge. A positive charge is near a positive electrically charged plate.

The presence of the electric field causes the positive charge to experience the electric force in the direction of the electric field so that the positive charge is accelerated to the right towards the negatively charged plate. The direction of the electric force to the right, in the direction of the motion of the charge, so that the electric force makes a positive work on the charge. Mathematically, the work done by the electric force on the positive charge is W = F d = q E d, where W = work, F = the electric force, d = distance between the two plates, q = positive charge, E = electric field.

After arriving near the negatively charged plate, if the positive charge is to be returned to its original position near the positively charged plate, an external force is required. When the positive charge is moved to the left towards the positively charged plate, the electric force remains directed to the right so that the electric force makes a negative work on the charge. Mathematically, the work done by the electric force on the positive charge is W = – F d = – q E d.

The total work done by the electric force on the positive charge, when the charge moves to the right, then move again to the left to its original position, is W = q E d – q E d = 0. If the net work is done by the force on the object, when the object moves away from its original position and then returns to its original position, equal to zero, then the force is a conservative force. Based on the explanation above, it can be concluded that the electric force is a conservative force.

### Electric force and electric potential energy

Work done by the conservative forces are related to changes in the potential energy. For example, the work done by the gravitational force on a mass object changes the gravitational potential energy of the mass object. Likewise, the work done by the electric force in an electric charge changes the electrical potential energy of the charge.

The positive charge in the homogeneous electric field

The two images below illustrate examples of work done by the conservative forces that cause changes in the potential energy. Explanation of the work done by the force of gravity and the changes in the gravitational potential energy is used as a comparison,

to facilitate understanding of the work done by the electric force and the changes in the electric potential energy. The image on the left shows an object falling freely towards the surface of the ground. When at the top, objects have maximum gravitational potential energy. When moving down, the gravitational force acts on the object. The direction of the gravitational force is the same as the direction of movement of the object that is down so that the gravitational force does positive work. When accelerated down, the height of the object decreases so that the gravitational potential energy of the object decreases. When arriving at the ground, the gravitational potential energy is minimum. It can be concluded that positive work done by the gravitational force on the object reduces the gravitational potential energy of the object. The gravitational potential energy is not lost but changes into the kinetic energy, which is indicated by the increase in the speed of the object when it moves down.

The figure on the right shows the positive charge near the positively charged plate. When near a positively charged plate, the electric potential energy has the maximum value. The presence of an electric field between the two plates causes the charge to be accelerated by the electric force from the positively charged plate to the negatively charged plate. When the charge moves to the right, the electric force is also in the direction of the charge displacement to the right, so that the electric force makes a positive work. During moving to the right, the kinetic energy of the charge increases while the electrical potential energy decreases.

Upon arrival near the plate with a negative charge, the potential electric energy has the minimum value. It can be concluded that the positive work done by the electric force on the charge reduces the electrical potential energy of the charge. Conversely, if the positive charge is moved back to its original position then the direction of the charge change to the left, opposite the direction of the electric force to the right. Because of the opposite direction, the electric force makes a negative work on the positive charge. When moving to the left, electrical potential energy increases. Thus, it can be concluded that the negative work done by the electric force on the charge increases the electrical potential energy of the charge.

### Negative charge in the homogeneous electric field Unlike the positive charge, the negative charge has the maximum electric potential energy when it is near the negatively charged plate and the minimum electrical potential energy when near the positively charged plate. Naturally, the electric charge moves from high potential to low potential, so the negative charge also moves from the negatively charged plate to the positively charged plate. The direction of displacement of the negative charge to the left, while the direction of the electric force to the right so that the electrical force makes a negative work. When moving to the left, the electric potential energy of the negative charge decreases and has a minimum value when the negative charge arrives near the positively charged plate. It can be concluded that the negative work done by the electric force reduces the electrical potential energy of the negative charge. The electrical potential energy is not lost but changes into kinetic energy which is characterized by increasing the speed of the charge when moving towards the positively charged plate.

Electric potential energy in the homogeneous electric field

The electric potential energy of a charge when the charge is in a certain position, its value cannot be known. But if the charge moves from one place to another, can be calculated the change of the electrical potential energy of the charge. So, what is meaningful is the change in potential energy. The changes in electric potential energy (ΔEP) can be known when the positive charge moves from the high potential (positively charged plate) to low potential (negatively charged plate).

For comparison, when the mango is on its stem, the mango has gravitational potential energy, but its value cannot be known. If the mango fruit is accelerated to the ground by gravitational force, the change of the gravitational potential energy of the mango can be known through calculation using the formula W = ΔEP = m g h,

where m = mass, g = gravitational acceleration, h = the distance between the mango and the surface of the ground.

Likewise, the changes of the electrical potential energy of a charge can be known when the electrical force accelerates the charge from one point to another. As previously explained, if the positive charge moves from the positively charged plate to the negatively charged plate,

the change of the electrical potential energy is calculated using the formula W = ΔEP = q E d, where q = the electric charge, E = the electric field and d = the distance between a place and another place. Likewise, if the negative charge moves from the negatively charged plate to the positively charged plate, the increase in the electrical potential energy of the negative charge is calculated using the formula W = ΔEP = q E d.

### The electric potential energy of the two point charges

The changes in electrical potential energy are not only experienced by the charge in a homogeneous electric field, but also the electric field produced by the single electric charge. Suppose there is a single charge Q which produce an electric field and a charge of q has a distance of r from the charge Q.  Q = electric charge that causes an electric field

q = electric charge that is displaced in the electric field produced by the charge Q

d = r = distance of charge q from charge Q.

If both charges have the same sign, + or -, then the two charges repel each other or keep away from each other so that the changes in potential energy are positive (electrical potential energy increases). This is like a mass object that moves upward away from the earth so that its height and the gravitational potential energy increase. Conversely, if the sign of both charges is not the same, the two charges pull each other or approach each other so that the change in potential energy is negative (the electric potential energy is reduced). This is like a mass object moving downward approaches the surface of earth so that its height and the gravitational potential energy are reduced.

Electric force is a conservative force, therefore the shape of the charge path does not affect the changes in the electrical potential energy. What influences the value of the changes in the electrical potential energy, is the initial position and the final position of the charge.

On the next topic will be studied about the electric potential, physical quantities that are strongly related to the electrical potential energy.