16.2. Electric Potential http://www.ck12.org
Check Your Understanding
1a. The electrical potential at the negative plate inFigure16.5 is defined as zero volts. What is the electrical
potential energy of a charge+q= 15. 0 μCat the positive plate if the electric field between the plates is 25. 0 NC?
The positive plate has position 6. 00 cm= 6. 00 × 10 −^2 maccording toFigure16.5.
Answer:PEpositive plate=qEx= ( 15. 0 × 10 −^6 C)
(
25. 0 NC
)
( 6. 00 × 10 −^2 m) = 3. 75 × 10 −^4 J1b. What is the change in the electrical potential energy∆PEof the charge+q= 15. 0 μCif its potential changes
from 1.5Vto 1.0V?
Answer: Just as in the case of a change in gravitational potential energy, the charge must lose potential energy, since
it gains kinetic energy.
The charge moves from the positionxi= 6. 00 × 10 −^2 m( 1. 5 V)to the positionxi= 4. 00 × 10 −^2 m( 1. 0 V).
∆PE=qExf−qExi=qE(xf−xi) =( 15. 0 × 10 −^6 C)(
25. 0
N
C
)
( 4. 00 × 10 −^2 m− 6. 00 × 10 −^2 m) =− 7. 50 × 10 −^6 J.1c. What is the work done on the charge by the electric field?
Answer:
Wf ield=−∆PE=−(− 7. 50 × 106 ) = 7. 50 × 106 JNotice that the electric field does positive work on the charge, since the electric force and the displacement of the
charge have the same direction.
We should recall a very important point: It is only the change in potential energy that is meaningful, whether we are
discussing the gravitational potential energy or the electrical potential energy.
- An electron placed at the negative plate of a parallel-plate conductor will move toward the positive plate. The
potential energy of the electron:
A. Decreases
B. Increases
C. Remains the same.
Answer: The correct answer is A. The electron is repelled by the negative charges of the conducting plate and
therefore gains kinetic energy. Just as an object that is dropped gains kinetic energy and loses potential energy, so
does the electron. Recall our discussion of the conservation of energy. As long as the total energy remains conserved,
the sum of the initial kinetic and potential energies must equal the sum of the final kinetic and potential energies:
KEi+PEi=KEf+PEf→∆KE=−∆PEThe gain in kinetic energy occurs due to the loss in potential energy.
In order for the charges of the same sign to be brought together, as in the example above, positive work must be done
by an external force against the electrostatic repulsion between the charges. The work increases the potential energy
stored in the electric field. When the charges are released, the potential energy of the field is converted into the
kinetic energies of the charges. The link below may be helpful in learning more about the work done upon charges
in electric fields.