Physics 102: Lecture 3 Electric Potential

1
Physics 102 Lecture 3Electric Potential
2
Recall from last lecture.

• E field has magnitude and direction
• E due to point charge Q EkQ/r2
• Force on charge q due to E FqE
• E and F are vectors
• Electric field lines
• Density gives strength ( proportional to
  charge.)
• Arrow gives direction (Start end on -)
• Conductors
• E0 inside a conductor

3
Overview for Todays Lecture

• Electric Potential Energy/ Work
• Uniform fields
• Point charges
• Electric Potential (like height)
• Uniform fields
• Point charges

07
4
Recall Work from P101

• Work done by the force given by
• W F d cos(q)
• Positive Force is in direction moved
• Negative Force is opposite direction moved
• Zero Force is perpendicular to direction moved
• Careful ask WHAT is doing work!
• Opposite sign for work done by you!
• Conservative Forces (not friction)
• Change in Potential Energy -Wconservative

09
5
Work and D Potential Energy
Gravity Uniform Electric Field

• Brick raised yi? yf

• charge q moved d to left
• FE qE (right)
• WE -qEd
• DUE qEd

• FG mg (down)
• WG -mgh
• DUG mgh

yf?
h
yi?
20
6
Work and D Potential Energy
W F d cos(q) Gravity Electric

• Brick raised yi? yf

• Charge moved 8 ? rf
• FE kq1q2/r2
• WE -kq1q2/rf
• DUE kq1q2/rf

• FG mg (down)
• WG -mgh
• DUG mgh

yf?
h
yi?
20
7
Preflight 3.1 ACT
C
A
B
-
Uniform E?

• In what direction does the force on a negative
  charge at point A point?
• left
• right
• up

53 43 4
Force on charge is in same direction of field if
POSITIVE and opposite direction if NEGATIVE.
10
8
Preflight 3.2ACT
C
-
-
-
-
A
B
-
Uniform E?

• When a negative charge is moved from A to C, the
  ELECTRIC force does
• positive work.
• zero work.
• negative work.

11
9
Preflight 3.2
motion
C
I would say zero because the path is
perpendicular to the field
A
B
Uniform E?

• When a negative charge is moved from A to C the
  ELECTRIC force does
• positive work.
• zero work.
• negative work.

10 85 05
11
10
Preflight 3.3 ACT
C
A
B
because the direction of the displacement is 180
degrees from direction of the force
-
Uniform E?

• When a negative charge is moved from A to B the
  ELECTRIC force does
• positive work.
• zero work.
• negative work.

66 7 21
13
11
Preflight 3.5 ACT
C
A
B
-
-
-
-
-
Uniform E?

• When a negative charge is moved from A to B, the
  electric potential energy of the charge
• Increases
• is constant
• decreases

D(EPE) -WE field Electric force did negative
work so electric potential energy increased.
Just like pushing mass uphill.
33 14 53
14
12
ACT Electric Potential Energy
AC W0

C
CB Wlt0
B
A
-
-
-
-
-
When a negative charge is moved from A to B, the
electric potential energy of the
charge (A) increases (B) is constant (C) decreases
1) The electric force is directed to bring the
electron closer to be proton. 2) Since the
electron ends up further from the proton the
electric field did negative work. 3) So the
electric potential energy increased
17
13
Work done by YOU to assemble 3 charges
Example

• W1 0

• W2 k q1 q2 /r

3.6 mJ
(9?109)(1?10-6)(2?10-6)/5

• W3 k q1 q3/r k q2 q3/r
• (9?109)(1?10-6)(3?10-6)/5 (9?109)(2?10-6)(3?1
  0-6)/5 16.2 mJ
• Wtotal 19.8 mJ
• WE -19.8 mJ
• DUE 19.8 mJ

3
5 m
5 m
2
1
5 m
Note the units and watch signs This is like
moving mass uphill
24
14
ACT Work done by YOU to assemble 3 negative
charges
How much work would it take YOU to assemble 3
negative charges?
Likes repel, so YOU will still do positive work!
3

• W 19.8 mJ
• W 0 mJ
• W -19.8 mJ

5 m
5 m
2
1
5 m
27
15
Preflight 3.11
1

5 m
5 m
Negative because i really hate physics. And i
dont know what is being ask in this question.
-

3
2
5 m
The total work required by you to assemble this
set of charges is (1) positive (2) zero (3) ne
gative
Bring in (3) zero work Bring in (2) negative
work Bring in (1) zero work (see next page for
explanation)
57 16 27
16
Preflight 3.11
Bring in (3) zero work because the other charges
are far away so the electric field due to those
charges is zero. Bring in (2) negative work.
why? Lets figure out the work done by the
electric field, which is just the negative of the
work done. The electric field felt by charge 2
is the field due to charge 3, which points toward
charge 3. So, we are moving charge 2 in the same
direction of the field. Therefore the work done
by the field is positive, so the work done by you
is negative Bring in (1) zero work. why? We
must do negative work due to charge 3 and an
equal amount of positive work due to charge 2, so
the net work is zero. Another way to think about
it is that the electric potential energy of
charge 1 is zero, since it has equal but opposite
contributions from charges 2 and3 Net result is
the sum of 0,negative, and 0 and is therefore
negative.
17
Preflight 3.11
Yet another way to work the problem Wyou -WE
Electric Potential Energy (EPE) of the three
charges. EPE kq1q2/r kq2q3/r kq1q3/r where
r is the separation between the charges (5 m).
All three terms have the same magnitude, since
all the charges have the same magnitude. The
first term is positive but the next two are
negative. Therefore, the EPE is negative, so
that Wyou is negative. As a practice exercise,
try calculating Wyou, assuming the magnitude of
each charge is 5 ?C. Answer -0.045 J.
18
Work and D Electric Potential
Gravity Uniform Electric Field

• Brick raised yi? yf

• charge q moved d to left
• DUE qEd change in electric potential energy
• DUE q(Ed) charge(q) x change in electric
  potential (Ed) VE
• Moving opposite to E increases VE

DUG mgh change in gravitational potential
energy DUG m(gh) mass (m) x change in
gravitational potential (gh) VG Moving from low
to high increases VG
m
m
20
19
Electric Potential

• Units Joules/Coulomb ?Volts (symbol V)
• Batteries
• Outlets
• EKG
• Really Potential differences
• Equipotential lines at same height
• Field lines point downhill
• from higher to lower potential
• V k q/r (distance r from charge q)
• V(8) 0

31
20
Preflight 3.7
Electric field points from greater potential to
lower potential

• The electric potential at point A is _______ at
  point B
• greater than
• equal to
• less than

55 26 19
32
21
Preflight 3.9
89
conductor

• The electric potential at point A is _______ at
  point B
• greater than
• equal to
• less than

The electric field within a conductor is zero,
and therefore, the potential for points A and B
are the same
33
22
Preflight Summary
Path
Vfinal - Vinitial
WE field
Charge
D U q DV
-
Negative
Positive
A ? B
Negative
Positive
Negative
-
A ? C
Zero
C ? B
Negative
-
35
23
Preflight Summary
Path
Vfinal - Vinitial
WE field
Charge
D EPE q DV
-
Negative
Positive
A B
Negative
Positive
Negative
Zero
Zero
-
A C
Zero
Zero
Zero
Negative
Positive
C B
Negative
-
Positive
Negative
35
24
ACT Electric Potential

C
B
A

• The electric potential at A is ___________ the
  electric potential at B.
• greater than
• equal to
• less than

1) Electric field lines point down hill
2) AC is equipotential path (perpendicular to
E) 3) CB is down hill, so B is at a lower
potential than (down hill from) A
38
25
Electric Potential Summary

• E field lines point from higher to lower
  potential
• For positive charges, going from higher to lower
  potential is downhill
• For negative charges, going from lower to higher
  potential is downhill
• For a battery, the terminal is at a higher
  potential than the terminal
• Positive charges tend to go downhill, from to
  -
• Negative charges go in the opposite direction,
  from - to

26
ComparisonElectric Potential Energy vs.
Electric Potential

• Electric Potential Energy (U) - the energy of a
  charge at some location.
• Electric Potential (V) - found for a location
  only tells what U would be if a charge were
  located there
• U Vq
• Usually we talk only about changes in potential
  or potential energy when moving from one location
  to another
• Neither U nor V has direction, just location.
  Sign matters!

27
Electric Potential due to a point charge
Example
not covered during lecture

• What is the electric potential V a distance r
  from a point charge, assuming V0 at ?
• answer V k q/ r

42
28
Two Charges
not covered during lecture
Example

• Calculate electric potential at point A due to
  charges
• Calculate V from 7mC charge
• Calculate V from 3.5mC charge
• Add (EASY!)
• V kq/r
• V7(9?109)(7?10-6)/5 12.6?103V
• V3(9?109)(-3.5?10-6)/5 -6.3?103V
• Vtotal V7V3 6.3?103V

A
4 m
6 m
Q7.0mC
Q-3.5 mC
WDUDVq (6.3?103V)(2mC) 12.6 mJ
How much work do you have to do to bring a 2 mC
charge from far away to point A?
46
29
ACT Two Charges
not covered during lecture

• In the region II (between the two charges) the
  electric potential is

1) always positive 2) positive at some points,
negative at others. 3) always negative
I
II
III
Q-3.5 mC
Q7.0mC
Very close to positive charge potential is
positive
Very close to negative charge potential is
negative
48
30
To Do

• Read 17.5-6
• Extra problems from textbook Ch 17
• Concepts 1-8
• Problems 1, 9, 15, 19, 23, 25
• Bring Problem Solver to discussion section
• Complete preflight before Monday 600am.

50