relating the change in potential energy to work done on the system,
ǻPEe = W
Step-by-step solution
We calculate the work done to move the charge q through the displacement ǻx.
SinceǻKE = 0, we may state that ǻPEe equals the work done on the system, and evaluate the result.
The solution shows that the system has a greater potential energy when q is in its final position. The external force did positive work on the
system, increasing its PE.
Step Reason
1. W = Fǻx definition of work
2. F = qE definition of field
3. W = qEǻx substitute equation 2 into equation 1
Step Reason
4. ǻKE = 0 particle stationary before and after
5. ǻPEe = W work done on system
6. ǻPEe = qEǻx substitute equation 3 into equation 5
7. evaluate
24.3 - Electric potential energy and work
For a given configuration of a system to have a certain “absolute” amount of potential
energy, a reference configuration with zero potential energy must be established.
Changes from that zero point will then be the measure of the potential energy of the
system.
With gravitational potential energy, an infinite separation between two masses is often
defined as the configuration that has zero potential energy. This convention is
frequently used for orbiting bodies. It is also common to use the convention that an
object at the Earth’s surface represents a configuration with zero gravitational potential
energy.
When analyzing electric potential energy, physicists usually state that a system of two
charges has zero electric potential energy when an infinite distance separates them.
The relationship between ǻPEe and work that was introduced previously can be
combined with this reference value to define a relationship between absolute PEe and
work, shown in Equation 1 on the right.
The relationship between the work W done by a system of two charges as one of
them moves in from an infinite separation, and the PEe of the system, is PEe = íW.
Why does this equation hold true? We already know that ǻPEe = íW, and when the
initial PEe is zero, then the change in potential energy is just the potential energy of the
system in its final configuration.
In Equation 2, we show you how to calculate the work done by the system as the
separation between charges changes. This equation can be derived using calculus.
Note that the signs of the charges do matter in the formula. If they are opposite,
applying the equation confirms that the system (the field) does positive work as the
particles approach one another. Conversely, the work done by the field is negative if
two like charges are moved closer to one another, as illustrated in the diagram.
In Equation 3, we combine the work and potential energy equations using an infinite
separation to define zero potential energy. Since zero is the result of dividing by infinity,
the 1/riterm “disappears” and only the fraction í1/rf remains in the final factor of the
work formula. Its negative sign cancels the one in the potential energy equation
PEe = íW, to yield the equation you see as Equation 3.
Note an implication of this equation: When the signs of the two charges are opposite,
the potential energy of the pair is negative. When they are the same, the potential
energy is positive.
Electric potential energy
To determine electric potential energy
·Set point of zero potential energy
·Infinite separation often used