Electric Potential
Electric Potential
Because the electric force can displace charged objects, it is capable of doing work. The presence of an electric field implies the potential for work to be done on a charged object. By studying the electric potential between two points in an electric field, we can learn a great deal about the work and energy associated with electric force.
Electric Potential Energy
Because an electric field exerts a force on any charge in that field, and because that force causes charges to move a certain distance, we can say that an electric field does work on charges. Consequently, we can say that a charge in an electric field has a certain amount of potential energy, U. Just as we saw in the chapter on work, energy, and power, the potential energy of a charge decreases as work is done on it:
Work
The work done to move a charge is the force, F, exerted on the charge, multiplied by the displacement, d, of the charge in the direction of the force. As we saw earlier, the magnitude of the force exerted on a charge q in an electric field E is = qE. Thus, we can derive the following equation for the work done on a charge:
Remember that d is not simply the displacement; it is the displacement in the direction that the force is exerted. When thinking about work and electric fields, keep these three rules in mind:
  1. When the charge moves a distance r parallel to the electric field lines, the work done is qEr.
  2. When the charge moves a distance r perpendicular to the electric field lines, no work is done.
  3. When the charge moves a distance r at an angle to the electric field lines, the work done is qEr cos .
Example
In an electric field, E, a positive charge, q, is moved in the circular path described above, from point A to point B, and then in a straight line of distance r toward the source of the electric field, from point B to point C. How much work is done by the electric field on the charge? If the charge were then made to return in a straight line from point C to point A, how much work would be done?
How much work is done moving the charge from point A to point B to point C ?
The path from point A to point B is perpendicular to the radial electric field throughout, so no work is done. Moving the charge from point B to point C requires a certain amount of work to be done against the electric field, since the positive charge is moving against its natural tendency to move in the direction of the electric field lines. The amount of work done is:
The negative sign in the equation reflects the fact that work was done against the electric field.
How much work is done moving the charge directly from point C back to point A?
The electric force is a conservative force, meaning that the path taken from one point in the electric field to another is irrelevant. The charge could move in a straight line from point C to point A or in a complex series of zigzags: either way, the amount of work done by the electric field on the charge would be the same. The only thing that affects the amount of work done is the displacement of the charge in the direction of the electric field lines. Because we are simply moving the charge back to where it started, the amount of work done is W = qEr.
Potential Difference
Much like gravitational potential energy, there is no absolute, objective point of reference from which to measure electric potential energy. Fortunately, we are generally not interested in an absolute measure, but rather in the electric potential, or potential difference, V, between two points. For instance, the voltage reading on a battery tells us the difference in potential energy between the positive end and the negative end of the battery, which in turn tells us the amount of energy that can be generated by allowing electrons to flow from the negative end to the positive end. We’ll look at batteries in more detail in the chapter on circuits.
Potential difference is a measure of work per unit charge, and is measured in units of joules per coulomb, or volts (V). One volt is equal to one joule per coulomb.
Potential difference plays an important role in electric circuits, and we will look at it more closely in the next chapter.
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