1. Electric Potential and Electric Potential Energy
Chapter 20
Electric Potential and Electric Potential Energy
Dr. Jie Zou
PHY 1161

2. Outline Electrical potential energy, U Electrical potential, V
Connection between electric field E and electric potential V
Energy conservation
Electrical potential of point charges
Dr. Jie Zou
PHY 1161

3. Electrical Potential Energy, U
Definition for U, the change in electrical potential energy of a charge:
U = Uf - Ui = -W
The work done by a conservative force (e.g., an electric force and force of gravity) is equal to the negative of the change in potential energy.
SI units: Joules (J)
Dr. Jie Zou
PHY 1161

4. Electrical Potential, V
Definition for V, the change in electric potential:
V = Vf – Vi = U/q0 = (-W)/q0
V is the change in electric potential energy per charge.
SI units: Joules/Coulomb (J/C) = Volt (V)
Relationship between U and V:
U = q0 V
Both are scalar quantities.
Another commonly used unit of energy is the electron volt (eV):
1 eV = (1.60x10-19 C)(1 V) = 1.60x10-19 J
Dr. Jie Zou
PHY 1161

5. Exercise 20-1
Find the change in electric potential energy, U, as a charge of (a) 2.20 x 10-6 C or (b) x 10-6 C moves from a point A to a point B, given that the change in electric potential between these points is V = VB – VA = 24.0 V.
Dr. Jie Zou
PHY 1161

6. Connection between Electric Field and Electric Potential
Connection between the electric field and the electric potential:
E = -V/s
V = -Es
The electric field depends on the rate of change of the electric potential with position.
The electric potential decreases as one moves in the direction of the electric field.
SI units for E: 1 N/C = 1 V/m
Dr. Jie Zou
PHY 1161

7. Example 20-1: Plates at Different Potentials
A uniform electric field is established by connecting the plates of a parallel-plate capacitor to a 12-V battery.
(a) If d = 0.75 cm, what is the magnitude of the electric field in the capacitor?
(b) A charge of +6.24x10-6 C moves from the positive plate to the negative plate. Find the change in electric potential energy.
(In electrical systems, we shall assume that gravity can be ignored, unless specifically instructed otherwise.)
Dr. Jie Zou
PHY 1161

8. Energy Conservation
Energy conservation: For a charged object in an electric field, its total energy must be conserved.
KA + UA = KB + UB, or
(1/2)mvA2 + UA = (1/2)mvB2 + UB
Example 20-2: What is (a) the mass of the charge and (b) its final kinetic energy?
Dr. Jie Zou
PHY 1161

9. Example 20-2: From Plate to Plate
Suppose a charge q = x 10-6 C is released from rest at the positive plate and that it reaches the negative plate with a speed of 3.4 m/s.
(a) What is the mass of the charge?
(b) What is its final kinetic energy?
Dr. Jie Zou
PHY 1161

10. The Electric Potential of Point Charges
Electric potential V produced by a point charge q at a distance r:
Conventionally, choosing the electric potential to be zero at infinity, V = kq/r
Electric potential energy U for point charges q and q0 separated by a distance r:
U = q0V = kq0q/r
Exercise 20-2: Find the electric potential by a point charge of 6.80x10-7 C at a distance of 2.60 m.
“+” charge
“-” charge
Dr. Jie Zou
PHY 1161

11. Homework #2
Chapter 20, P , Problems: #2, 4, 19 (Physics, Walker, 4th edition).
Dr. Jie Zou
PHY 1161