Download electric potential

Monday, February 18, 2013
LESSON 7:
ELECTRIC POTENTIAL
Announcements
HW #6 due today
HW #7 due tomorrow
Modern Phys #2 due tomorrow
 Ignore the lab simulation info on HW sheet
HW Quiz TUESDAY!!!
Lunch Bunch this week:
 Photoelectric Lab simulation
(Details to come Tuesday)
AP Physics B Course Objectives
III.A.2. Electric Field & Electric Potential
b) Students should understand the concept of
electric potential, so they can:
(1) Determine the electric potential in the vicinity of one or more point
charges.
 (2) Calculate the electrical work done on a charge or use conservation of
energy to determine the speed of a charge that moves through a specified
potential difference.
 (4) Calculate the potential difference between two points in a uniform
electric field, and state which point is at the higher potential.
 (5) Calculate how much work is required to move a test charge from one
location to another in the field of fixed point charges.
Student Objectives
Students will be able to:
1)
2)
read and interpret equipotential maps.
apply energy conservation to electrostatic situations
Review: Electric Potential Energy
Potential energy configuration of two
charges
For spherically symmetric charges
Electrostatic forces spontaneously do
positive work to decrease EPE.
External forces are necessary to increase
EPE.
EPE and Work
For ANY force:
W = F ∆r cos θ
For electrostatic forces: WE = FE ∆r cos θ
For conservative forces: Wc = - ∆U
Electrical Potential and
Potential Energy
Electric Potential is Electric Potential Energy
per unit charge.
UE
V
q
Electric Potential Difference is the change in
electric potential energy per unit charge.
U E
V 
q
Unit: Volts
Common term: voltage
Electric Potential Difference
r = 1.0 m
q1 = 1.0 C
1.0 1.0
1.0
ΔU = UB – UA
ΔU = (1/2 k – 1 k)
ΔU = –1/2 k
r = 1.0 m
q2 = 1.0 C
B
A
1.0 1.0
2.0
1⁄2
ΔVAB = ΔU / q2
ΔVAB = (-1/2k) / (1.0 C)
ΔV = –(1/2 k) V
The positive charge naturally moves in the direction of DECREASING U.
Positive charges move to DECREASE their electric potential (V).
Electric Potential Difference
rA = 1.0 m
q1 = 1.0 C
rB = 0.5 m
B
q2 = -1.0 C
1.0
1.0
1.0
ΔU = UB – UA
ΔU = (– 2 k – (– 1 k))
ΔU = – k
A
1.0
1.0
0.5
2
ΔVAB = ΔU / q2
ΔVAB = (- k) / (-1.0 C)
ΔV = +(k) V
The negative charge naturally moves in the direction of DECREASING U.
Negative charges move to INCREASE their electric potential (V).
Electrical Potential and
Potential Energy
Spontaneous movement will decrease UE.
∆V = ∆U / q
Positive charges like to DECREASE their
potential (V < 0)
Negative charges like to INCREASE their
potential. (V > 0)
Sample problem 7.1:
A 3.0 μC charge is moved through a potential difference of
640 V. What is its potential energy change?
Electric Potential due to
multiple charges
 The electric potential at
any point in space is the
scalar sum of the
potentials due to each
charge
V = V1+ V2 +V3
Electric Potential of
Spherically Symmetric Charges
Characteristics of Equi-potential
Surfaces
Characteristics of
Equipotential Surfaces
About Equipotential Maps…
1. The potential difference
between any two points
along the same
equipotential line is zero.
2. Electric field lines always
point in the direction of
decreasing electric
potential.
3. Electric field lines are
always perpendicular to
the equipotential lines.
4. The closer the
equipotential lines are to
one another, the steeper
the gradient of the
potential.
Sample problem 7.2:
Suppose a 2mC charge is moved from point b to point c.
a) What is its potential energy change?
b) What about if a -3mC charge does the same thing?
Conservation of Energy
Review
In a conservative system, energy changes from
one form of mechanical energy to another.
U1  K1 U2  K2
Sample problem 7.3:
If a proton is accelerated through a potential difference of
-2,000 V, what is its change in potential energy?
How fast will this proton be moving if it started at rest?
Sample Problem 7.4:
A proton at rest is released in a uniform electric field. How
fast is it moving after it travels through a potential difference
of -1200 V? How far has it moved?
Sample Problem 7.5:
Suppose an electron is moving at 200,000 m/s when it enters
a region where its electric potential begins changing. Through
what potential difference must it travel before it comes to rest
(assuming its motion is aligned with the field).