Electric Potential

Review: Work and Energy Work is defined as the product of force F times displacement d. Work is defined as the product of force F times displacement d. Work = F x d; Units: Joules Potential Energy is defined as the ability to do work by virtue of position or condition. (Joules)

Once again, we’ll use gravity as an analogy…

Work in a gravitational field When gravity does work on an object to move it in the direction of the gravitational field, then the object loses potential energy. On the other hand, energy would be required to move a massive object against a gravitational field. Energy in the form of work would have to be imparted to the object by an external force in order for it to gain this height and the corresponding potential energy.

Work (as applied to gravity) The important point to be made by this gravitational analogy is that work must be done by an external force to move an object against nature - from low potential energy to high potential energy. On the other hand, objects naturally move from high potential energy to low potential energy under the influence of the field force. It is simply natural for objects to move from high energy to low energy.

Another example… In which drawing does the bow have more potential energy? Was an external force required to get the bow to a position of higher potential energy?

Work in an Electric Field In a similar manner, to move a charge in an electric field against its natural direction of motion would require work. The exertion of work by an external force would in turn add potential energy to the object. The natural direction of motion of an object is from high energy to low energy; but work must be done to move the object against nature. On the other hand, work would not be required to move an object from a high potential energy location to a low potential energy location. The field itself does that!

Consider the diagram above in which a positive source charge is creating an electric field and a positive test charge is being moved against and with the field. In Diagram A, the positive test charge is being moved against the field from location A to location B. Moving the charge in this direction would be like going against nature. Thus, work would be required to move the object from location A to location B and the positive test charge would be gaining potential energy in the process. This would be analogous to moving a mass in the uphill direction; work would be required to cause such an increase in gravitational potential energy.

In Diagram B, the positive test charge is being moved with the field from location B to location A. This motion would be natural and not require work from an external force. The positive test charge would be losing energy in moving from location B to location A. This would be analogous to a mass falling downward; it would occur naturally and be accompanied by a loss of gravitational potential energy. The high energy location for a positive test charge is a location nearest the positive source charge; and the low energy location is furthest away.

What is the source charge is negative? The low energy location for a positive test charge is a location nearest a negative source charge and the high energy location is a location furthest away from a negative source charge.

Check your understanding: Electrical potential energy is the energy a charged object has due to its a. movement in an electric field. b. energy. c. position in an electric field.

Check your understanding: If a small positive charge is brought near a large, positively charged conductor, what happens to its electrical potential energy? a. Because the charges are the same the energy is reduced. b. Because they repel, its potential energy will increase. c. Because the charges are the same, the energy will not be changed.

1.Is the source charge positive or negative? How do you know? 2.If you pushed a positive test charge in the direction of the blue arrow, would it take work? 3.If you pushed the positive test charge in the direction of the blue arrow, would it gain or lose electric potential energy? 4.What would happen if you released the charge after pushing it toward the center?

Electric Potential Consider the electric field created by this large positive charge. The direction of the electric field is in the direction that a positive test charge would be pushed; in this case, the direction is outward away from sphere. Work would be required to move a positive test charge towards the sphere against the electric field. The amount of force involved in doing the work depends on the amount of charge being moved. The greater the charge on the test charge, the greater the repulsive force and the more work that would have to be done on it to move it the same distance. If two objects of different charge - with one being twice the charge of the other - are moved the same distance into the electric field, then the object with twice the charge would require twice the force and thus twice the amount of work. This work would change the potential energy by an amount that is equal to the amount of work done. Thus, the electric potential energy is dependent upon the amount of charge on the object experiencing the field and upon the location within the field.

So far we’ve talked about Electric Potential Energy, but Electric Potential isn’t quite the same thing.

Electric Potential Electric potential energy depends on the charge of the object experiencing the electric field. The greater the charge on the “test charge,” the greater the electric potential energy. To continue the gravity analogy, a boulder sitting on top of a cliff has more potential energy than a pebble sitting at the same spot.To continue the gravity analogy, a boulder sitting on top of a cliff has more potential energy than a pebble sitting at the same spot.

Electric Potential Electric potential is purely location dependent. Electric potential is the potential energy per charge.

Check your understanding: When work is done on a positive test charge by an external force to move it from one location to another, potential energy _________ (increases, decreases) and electric potential _________ (increases, decreases).

Answer the questions for each diagram: Is work required to move the test charge from point A to point B? _____ Does the test charge gain or lose potential energy? __________________ Which point (A or B) has the greatest electric potential? _____ potential.

True or False? Electric potential at a point is a property of the space, whereas electric potential energy cannot exist unless a charge is placed at that point.

The SI Unit of Potential (Volt) From the definition of electric potential as P.E. per unit charge, we see that the unit must be J/C. We redefine this unit as the volt (V). A potential of one volt at a given point means that a charge of one coulomb placed at that point will experience a potential energy of one joule.

CONCLUSION: Electric Potential