# Get the Knowledge that sets you free...Science and Math for K8 to K12 students

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## Electric Potential

Are you safe inside a car on a stormy night? Have you ever wondered what would happen if you were struck by lightning while in a car on a stormy night? What is the cause of this lightning? Lets learn more from such applications that we face in everyday life.

## After completing the topic, the student will be able to:

• Explore and validate the concept of electric potential based on various daily life scenarios.
• Discuss and differentiate between electric potential energy and gravitational potential energy.
• Explore electrical potential of a point charge and develop electrical potential difference between two point charges and also for a group of point charges.
• Discuss, explore and relate equipotential of a surface to the electric field strength.
• Explore and expand bio–medical applications of the electrical potential difference in recording the heart beat of a person and analyze the electrical impulses due to visual or auditory stimuli.
Object moving in a uniform gravitational field
• The work done on a basketball moving in a uniform gravitational field.
• The work done by the gravitational force is the same for any path from a to b: w = – Δ U = mgh
Introduction

In mechanics, potential energy of a body is described in detail; it was due to its position or internal atomic arrangement. The two main types of potential energy are elastic and gravitational potential energies. When there is no external source of energy, if an object is in motion, its kinetic energy and its potential energy are interchanged between each other and the object’s energy is conserved. For example, motion of a pendulum bob or motion of a ball falling from a height.

When a charge is moving in an electric field that is produced by a source charge, what happens to its potential energy and kinetic energy? Consider a ball held at a height h. Its gravitational potential energy is mgh. If the ball is released, it will fall towards the earth, which has a gravitational potential energy of zero. The ball moves from a higher potential energy level to a lower potential level.

Its potential energy mgh is converted to kinetic energy 1/2mv2. Now replace the ball with a negative charge –q which has a mass mq. Its gravitational potential is mqgh. It will also behave in the same manner as the ball when it falls towards the earth. Place a charge +Q on an insulating pole at a horizontal distance and distance h from –q. The negative charge –q is placed equidistant from the earth and the positive charge +Q. What would happen to the motion of the negative charge?

The negative charge –q would of course be attracted to +Q, since the electric force or Coulomb force is at least 1038 times stronger than the gravitational force.

Electric potential energy of a charge in analogy with the elastic potential energy of a spring
• The spring has more elastic PE when compressed.
• The small charge similarly has more PE when pushed closer to the charged sphere. In both cases the increased PE is the result of work required to reach the closer location.
Electric potential energy

What can we say about the potential energy of the negative charge when it is moving towards the positive charge? We observe that its gravitational potential energy remains the same (mqgh). Since electric or Coulomb force is making the negative charge move, we say that the Coulomb force is arising due to energy, which we name it as electric potential energy.

Motion of the negative charge in an electric field of the positive charge can be compared to the motion of the ball in a gravitational field of the earth. We say that the negative charge moves from a higher electrical potential energy level to a lower electrical potential energy level.

If the ball has to be lifted from height h to a higher height h1, (h1 > h), we have to supply energy to the ball. The energy is used for working against the gravitational force. The potential energy of the ball at the new height is mgh1 and it has increased. Similarly, how can the electrical potential energy of –q be increased? If we shift –q away from +Q (the level of zero potential energy), this can be possible. If we move –q from its position to the left, the potential energy level of –q increases.

Replace –q with +q. Since +q is a positive charge, it will get automatically repelled by the source charge +Q (like charges repel each other). Now we have a scene opposite to –q. The potential energy decreases when +q is moving away and the potential energy increases when +q comes closer to +Q. This is because work has to be done by an external force to push +q towards +Q and the energy is stored as potential energy.