1. Electric Potential Energy and The Electric Potential
Physics
Fall 2016
Chapter 19
Electric Potential Energy and The Electric Potential
Eugene Danquah.

2. Electric Potential Energy and The Electric Potential
Work done moving a charged particle in an electric field can result in the particle gaining either potential or kinetic energy or both.
We will discuss charges at rest, thus concentrate on only changes in potential energy.
Recall in Phys 131, when a ball is lifted against the force of gravity, work is done on the ball and thus the gravitational potential energy of the ball is increased. (Refer to Figure 1).

3. Electric Potential Energy and The Electric Potential2
+ ve 2 g E 1
+ ve 1
Earth
- ve
Figure 1

4. Electric Potential Energy and The Electric Potential
A similar situation arises with two unlike charges.
Two unlike charges attract each other so when you pull one away from the other, you must do work .
When this work is done, it is stored as electric potential energy.

5. Electric Potential Energy and The Electric Potential
We defined electric field E as force per unit charge (F/q).
In a similar vein, we will define a quantity known Electric Potential V at a given point as the electric potential energy (EPE) of a small test charge q situated at that point divided by the charge itself.
V = EPE/q. Unit of electric potential is J/C or Volt (V).
The electric potential V between two points, a distance d apart in a uniform field if given by V= E*d

6. Electric Potential Energy and The Electric Potential
Example:
Consider a point charge of 2 coulombs in an electric field of 0.5 N/C as shown in the diagram below.
What is the change in electrical potential energy in moving the change from point A to B which is 0.5 m away.
What is the change in electric potential moving the charge from point A to B which is 0.5 m away. + + + B A +

7. Electric Potential Energy and The Electric Potential
Note:
A positive electric charge accelerates from a region of higher potential toward a region of lower potential.
A negative charge accelerates from a region of lower potential toward a region of higher potential.

8. Electric Potential Energy and The Electric Potential
Examples:
Example 1:
Two large charged parallel plates are 5 cm apart. The magnitude of the electric field between them is 500 N/C.
What is the potential difference between the plates?
What work is done moving a charge of 1.6 micro Coulomb from one plate to another?

9. Electric Potential Energy and The Electric Potential
Examples:
Example 2:
A voltmeter measures the potential difference between two large parallel plates to be 60 V. The plates are 3 cm apart. What is the magnitude of the electric field between them?

10. Electric Potential Energy and The Electric Potential
Practice Questions
The electric field intensity between two large, charged, parallel metal plates is 8000 N/C. The plates are 0.05 m apart. What is the potential difference between them?
A voltmeter reads 500V when placed across two charged , parallel plates. The plates are 0.02 m apart. What is the electric field between them?
What is the potential difference applied to two metal plates 0.5 m apart if the electric field between them is 3000 N/C.

11. Electric Potential Energy and The Electric Potential
Electric Potential Difference Created By Point Charges
The electric potential of a point charge is given by V = kq/r.
Consider a point charge q in a vacuum and a point P at a distance r from the point charge. The potential at point P due to the charge is given by V = kq/r
Negative charges will contribute a negative potential and positive charges will contribute a positive potential. r q P

12. Electric Potential Energy and The Electric Potential
Practice Questions.
4. What is the potential at each of the following distances from a charge of 2 micro Coulomb.
r = 10 cm; b. r = 50 cm.
c. How much work is required to carry a 0.05 micro Coulomb charge from the point at r = 50 cm to that at r = 10 cm.
d. Suppose a proton is released at r = 10 cm. How fast will it be moving as it passes a point at r = 50 cm?

13. Electric Potential Energy and The Electric Potential
Practice Questions.
The following point charges are placed on the x-axis: +2 micro Coulomb at x = 20 cm, -3 micro Coulomb at x = 30 cm, -4 micro Coulomb at x = 40 cm. Find the total potential on the axis at x = 0 cm.
In the figure below, the charge at A is +200 pico Coulomb and the charge at B is -100 pico Coulomb.
a. Find the electric potentials at points C and D.
b. How much work must be done to transfer a charge of +500 micro Coulomb from point C to point D.

14. Electric Potential Energy and The Electric Potential
Practice Questions. 6 contd. D C
- 100 pC
+200 pC
20cm
60 cm
20 cm

15. Electric Potential Energy and The Electric Potential
Equipotential Surfaces and Their Relation to The Electric Field.
Equipotential Surface is a surface on which the electric potential is the same everywhere.
The net force does no work as a charge moves on an equipotential surface.
The electric field created by any charge or group of charges is everywhere perpendicular to the associated equipotential surfaces and points in the direction of decreasing potential.

16. Electric Potential Energy and The Electric Potential
Capacitors and Dielectrics
A capacitor consists of two parallel plates with opposite charges and an insulating material known as a dielectric in between them.
A capacitor’s primary function is to store electric charge.
The relationship between the magnitude of the charge q on each plate of the capacitor and the potential difference V between the plates is given by q = CV where C is Capacitance. (Unit is Coulomb/Volt also known as the Farad)

17. Electric Potential Energy and The Electric Potential
Capacitors and Dielectrics
q is magnitude of the charge on either conductor
C is capacitance
V is magnitude of potential difference between conductors.

18. Electric Potential Energy and The Electric Potential
Capacitors and Dielectrics
The capacitance of a parallel-plate capacitor whose opposing plate faces, each of Area A, are separated by a small distance d is given by:
C = KЄoA/d
K is a dimensionless dielectric constant
Єo is 8.85 X C2/N.m2

19. Electric Potential Energy and The Electric Potential
Capacitors and Dielectrics
The energy PE stored in a capacitor of capacitance C that has a charge q and a potential difference V is given by
PE = ½ qV or PE = ½ q2/C

20. Electric Potential Energy and The Electric Potential
Capacitors and Dielectrics Practice Questions 7. What is the charge on a 300 pF capacitor whenit is charged to a voltage of 1.0 kV. 8. A metal sphere mounted on an insulating rod carries a charge of 6 nC when its potential is 200V higher than its surroundings. What is the capacitance of the capacitor formed by the sphere and its surroundings?

21. Electric Potential Energy and The Electric Potential
Capacitors and Dielectrics Practice Questions 9. A 1.2 µF capacitor is charged to 3 kV. Compute the energy stored in the capacitor.