1. -Electric Potential Energy -Electric Potential -Electric Potential Difference(Voltage)
AP Physics C
Mrs. Coyle

2. DUA->B= UB-UA= - Wfield
Gravitational Potential Energy of the “Earth’s Field – Test Mass” System A
Higher Potential Energy
DUA->B= UB-UA= - Wfield
The negative sign indicates that
when the field does positive work
the system loses potential energy.
Lower Potential Energy B

3. Electric Potential Energy of the “Electric Field - Test Charge” System+ A
Higher Potential Energy
DUA->B= UB-UA= - Wfield AB
The negative sign indicates that when the field does positive work the system loses potential energy.
F=qoE
Wfield AB = Fdcos(q)
Wfield AB =qoEdcos(q)
Lower Potential Energy B

4. Change in Electric Potential Energy: (Final PE- Initial PE)
DUA->B= UB-UA= - Wfield = -qoEdcos(q)
Change in Electric Potential: (Final PE- Initial PE)
DVA->B= VB-VA = UB-UA = - Wfield qo qo

5. The Electric Force is Conservative
The force, F = qoE, caused by the electric field and experience by the charge is conservative. That is:
The work done by the conservative force does not depend on the path taken.
A trip back to the original position would have a change in energy of zero.

6. For an infinitesimal displacement vector , ds, that is oriented tangent to a path through space:
Wfield AB = F.ds = qoE.ds
Wfield AB =-ΔU = qoE.ds ds

7. Change in potential energy of the system
Change in potential (Voltage) of the system

8. Electric Potential vs Potential Difference
The potential energy per unit charge, U/qo, is the electric potential
The potential is independent of the value of qo
The potential has a value at every point in an electric field
The electric potential is :
Potential Difference (Voltage):

9. Electric Potential Difference (Voltage ):
work per unit charge required to move a charge
between two positions in an electric field.
Scalar
Unit: 1 Volt = 1 J / C
It takes one joule of work to move a 1-coulomb charge through a potential difference of 1 volt

10. Electric Potential Energy
Which point is at a higher electric potential energy location? Consider a positive test charge.
Note: Electric Field lines point to the lower potential energy.

11. Electric Potential Which point is at a higher electric potential?
Note: Electric Field lines point to the lower potential.

12. Electron-Volts A unit of energy
One electron-volt is defined as the energy a charge-field system gains or loses when a charge of magnitude e (an electron or a proton) is moved through a potential difference of 1 volt
1 eV = 1.60 x J
Remember that e=1.60 x C

13. Using Conservation of Energy
Using conservation of energy, if the voltage difference is known, the potential energy difference can be calculated for a given charge.
If all the potential energy is converted to kinetic energy, then final speed can be calculated.

14. Summary of Charged Particle Released from Rest in a Uniform Field
A positive charge released from rest moves in the direction of the electric field.
The change in potential is negative.
The change in potential energy is negative.
The force and acceleration are in the direction of the field.

15. Potential in a Uniform Electric Field
AB
ΔVAB = -EdAB
E= -ΔVAB/dAB
The negative sign indicates that when the field does positive work the system loses potential energy.
Another unit for electric field is: 1 V/m= 1 N/C
We can interpret the electric field as the change of the electric potential with position.

16. Equipotential surfaces are always perpendicular to field lines.
Equipotential surface is a surface consisting of a continuous distribution of points having the same electric potential.
Equipotential surfaces are always perpendicular to field lines.

17. Ex.#1 a) What is the potential difference from F to B?
b) Where is the electric field the strongest?
c) Calculate the electric field at A.
d) What is the direction of the electric field at D?

18. Ex #2
What work does an outside force have to do to move a +2nC charge from E to F?
What work does an outside force have to do to move a 2nC charge from E to F to G and back to E?
What work does an outside force have to do to move a +2nC charge from E to H?
What work does an outside force have to do to move a -2nC charge from E to F?

19. Ex. #3 If V=12Vand d=0.2m find E. Draw 3 equipotentials.
Find the distance between the equipotentials.
What is the voltage difference between the positive plate and the next equipotential?
What speed would be reached by a proton accelerated across the two plates?