Home >> Science & Nature >> Science

What Is the Potential Electric Energy of a Charged Object?

The concept of potential energy is a strange one, but it's a useful one. If you see twin toddlers, one running around shouting and playing and the other sitting and reading a picture book, you'd say the physically active twin was energetic, and the other was a bit sedate. A physicist can look at two identical charged particles in an electric field, with one moving and the other remaining stationary. The physicist would say the moving particle has kinetic energy, and the other one has energy, too: potential energy.

The Concept of Potential Energy
- Imagine a tennis ball resting on a table. Now imagine you're holding a tennis ball at the same height. Neither of the balls is moving, so neither has any kinetic energy. If you let the ball loose from your hand, it will start moving. When it hits the ground, it will have a velocity that depends upon the height you dropped it from. However, all you did was let it go. You didn't add energy to it. Because the concept of conservation of energy is central to physics, physicists proposed that the ball had potential energy that was converted to kinetic energy. The ball still on the table, the one that hasn't moved at all, still has potential energy.
The Usefulness of the Concept
- Objects that demonstrate no visible sign of energy can be invested with potential energy that can be converted to motion.
  
  The motion of a dropped ball can be calculated with Newton's laws of motion. The speed when the ball hits the ground is the sqrt (2 * h * g); where h is the height and g is the acceleration of gravity. If instead you say that the kinetic energy at the bottom --- (1/2) * m * v^2 --- equals the potential energy at the top --- m g h --- then the velocity at the ground is sqrt (2 * h * g). Therefore, even though the concept of potential energy is strange, it can provide an accurate method for solving problems. This brings you to the electric field and the concept of electric potential energy.
The Electric Field
- Two electric charges exert a force on each other. You can calculate the effects knowing the forces, in the same way you can use Newton's laws to calculate the motion of a falling object. However, similar to the discussion in the last section, you can also think of the problem in a different way. The first charge will have an effect all through space, and you can think of that effect as an electric field. One way of interpreting the electric field is as an entity that creates a potential energy for any other charges that are brought into the field. Any force on a charge will be due to changes in the potential energy of a charge in the field.
The Energy of a Charge in the Electric Field
- Coulomb's law says the force on one charge, q, due to another charge, Q, is proportional to (qQ / r^2), where r is the distance between the two charges. The amount of work done to move the charge from one spot to another is equal to the force times the distance. It's also equal to the change in potential energy. The work is given by (qQ) times the integral from r1 to r2 of (1/r^2). The answer is qQ*((r1 - r2) / (r1 * r2). So this must be the difference in the potential energy between r1 and r2. Starting from qQ*((r1 - r2) / (r1 * r2), you get to qQ * ((r1/(r1 * r2) - (r2/(r1 * r2)), which equals qQ/r2 - qQ/r1. That is the difference in potential energy, U(r2) - U(r1), so the potential energy of a charge in an electric field U(r) = constant*qQ/r.

Science