Download Q - Purdue Physics

• Exam 1 on Feb 17 (Tuesday), 8-9:30 PM,
PHYS Rm 112.
1
Clicker Question 1
Which arrow best represents the field at the “X”?
A)
B)
C)
D)
E)
E=0
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Question 2
Which one of these statements is false?
A. The electric field of a very long uniformly charged rod
has a 1/r distance dependence.
B. The electric field of a capacitor at a location outside
the capacitor is very small compared to the field
inside the capacitor.
C. The fringe field of a capacitor at a location far away
from the capacitor looks like an electric field of a point
charge.
D. The electric field of a uniformly charged thin ring at
the center of the ring is zero.
8
Infinitesimals and Integrals in Science
Q
Charge distribution is not continuous
Charge distribution is not exactly uniform
Mathematical idealization
Works well for macroscopic systems
Atomic force microscope: scans
microscopic structure using variations in
charge density on surface
9
Chapter 17
Electric Potential
10
Electric and Gravitational Potential Energy
1
q2
q1q2
F
r̂
2
4 0 r
m1m2
F  G 2 rˆ
r
q1
m2
m1
1
q1q2
U el 
40 r
m1m2
U grav  G
r
11
Electric Potential Energy of Two Particles
r12
Potential energy is associated with pairs of interacting objects
Energy of the system:
1. Energy of particle q1
q2
2. Energy of particle q2
3. Interaction energy Uel
q1
E = E1+E2+Uel
To change the energy of particles we have to perform work.
E1  E2  Wext  Wint  Q
Wext – work done by forces exerted by other objects
Wint – work done by electric forces between q1 and q2
Q – thermal transfer of energy into the system
14
Electric Potential Energy of Two Particles
E1  E2  Wext  Wint  Q
q2
r12
E1  E2  Wint  Wext  Q
Uel  -Wint
q1
if (mc )  0
K system  Uel  Wext  Q
2
Total energy of the system can be changed (only) by external forces.
Work done by internal forces:
f
U el  Wint    Fint  dr
i
16
Electric Potential Energy of Two Particles
Fint
f
U el  Wint    Fint  dr
i
q2
f
1 q1q2
U el  
rˆ12  dr12
2
4 0 r12
i
r12
f
1 q1q2
U el   
dr12
2
40 r12
i
q1

F
1
q1q2
rˆ12
2
40 r12
1
f
1
U el  
q1q2  2 dr12
40
r
i 12
f
 1
U el  
q1q2  
40
 r12 i
1
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Electric Potential Energy of Two Particles
 1 q1q2 
Uel   
 4 0 r12 
Meaning of U0:
r12
1
q1q2
U el 
 U0
4 0 r12
U el  U 0
Choose U0=0 – no potential energy if r12 (no interaction)
q2
q1
Potential energy = amount of work
the two charges can do when moved
away from each other to 
q2
q1
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Electric Potential Energy of Two Particles
q2
1 q1q2
U el 
(joules)
40 r12
q1
Uel > 0 for two like-sign charges
(repulsion)
q2
q1
Uel < 0 for two unlike-sign
Charges (attraction)
20
Electric and Gravitational Potential Energy
1
q2
q1q2
F
r̂
2
4 0 r
m1m2
F  G 2 rˆ
r
q1
m2
m1
1
q1q2
U el 
40 r
m1m2
U grav  G
r
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Three Electric Charges
Interaction between q1 and q2 is
independent of q3
There are three interacting pairs:
q1  q2
U12
q2  q3
U23
q3  q1
U31
U= U12+ U23+ U31
1
q1q2
1 q2 q3
1 q1q3
U el 


4 0 r12
4 0 r23
4 0 r13
26
Multiple Electric Charges
q1
q3
q6
q2
q4
Each (i,j) pair interacts:
potential energy Uij
q5
1 qi q j
U el  U ij  
i j
i  j 40 rij
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Electric Potential
Electric potential  electric potential energy per unit charge
U el
V
q
Units: J/C = V (Volt)
Volts per meter = Newtons per Coulomb
Alessandro Volta (1745 - 1827)
Electric potential – often called potential
Electric potential difference – often called voltage
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V due to One Particle
U el
V
q
q2
Single charge has no electric
potential energy
Single charge has potential to
interact with other charge –
it creates electric potential
1
q1q2
U el 
40 r
1
q1
VB 
40 r
probe charge
J/C, or Volts
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V due to Two Particles
Electric potential is scalar:
VC  VC ,1  VC , 2
1
q1
1 q2


40 r13 40 r23
Electric potential energy of the system:
q3
U sys
1 q1q2
 U12 
40 r12
If we add one more charge at position C:
U sys
1 q1q2  1 q1
1 q2 
 U12  VC q3 


q3

4 0 r12  4 0 r13 4 0 r23 
U sys
1 q1q2
1 q1q3
1 q2 q3



 U12  U13  U 23
40 r12
40 r13 40 r23
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V at Infinity
1 q1
V
40 r
r, V=0
Positive charge
Negative charge
32
Exercise
What is the electrical potential at a location 1Å from a proton?
1Å


19
1.6

10
C
1 q1 
9 Nm 
V
  9  10
 14.4 J/C  14.4 V
2 
10
40 r 
C 
10 m
2


What is the potential energy of an electron at a location
1Å from a proton?


19
18
U el  Vq  14.4 J/C 1.6  10 C  2.3  10 J
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Exercise
2Å
1Å
What is the change in potential in going from 1Å to 2Å from the proton?
o
o



V  V 2 A  V 1A  7.2 V


 
What is the change in electric potential energy associated with
moving an electron from 1Å to 2Å from the proton?
o
o
o
o







Uel  Uel 2 A  Uel 1A  qV 2 A  qV 1A  qV


 


 


Uel  1.6  1019 C 7.2 J/C  1.15  1018 J
Does the sign make sense?
34
Electric Potential Difference in a
Uniform Field
Electric potential  electric potential energy per unit charge
U electric
U electric
 qV, V 
q
Units: J/C = V (Volt)
Volts per meter = Newtons per Coulomb
Electric potential, V – often called potential
Electric potential difference, V – often called voltage
40
V   E  l  ( Ex x  E y y  Ez z )
If we multiply through by q, we recover the relation between
the change in potential energy and work done on q by the 41
internal force.
Example
300
V   E  l   E l cos   100 (N/C)  2 (m) cos(30o )  173 volts
42
Example
x
An electron traveling to the right enters capacitor through a small hole
at A. Electric field strength is 2x103 N/C. What is the change in the
electron’s potential energy in traveling from A to B? What is its
change in kinetic energy? AB)= 4mm
Uelectric  F  l  (eEx )x  eEx x
= (1.6x10-19 C)(2x103 N/C)(0.004m) =1.3x10-18 J
K  Uelectric = -1.3x10-18 J
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Sign of the Potential Difference
U el  qV
The potential difference V can be positive or negative.
The sign determines whether a particular charged particle will gain
or lose energy in moving from one place to another.
If qV < 0 – then potential energy decreases and K increases
If qV > 0 – then potential energy increases and K decreases
Path going in the direction of E: Potential is decreasing (V < 0)
Path going opposite to E: Potential is increasing (V > 0)
Path going perpendicular to E: Potential does not change (V = 0)
44
Question 1
A proton is free to move from right to left
in the diagram shown. There are no other
forces acting on the proton. As the proton
moves from right to left, its potential energy:
A)
B)
C)
D)
Is constant during the motion
Decreases
Increases
Not enough information
V1 < V2
Sign of the Potential Difference
U el  qV
If freed, a positive charge will
move to the area with a lower
potential:
Vf – Vi < 0
U el  qV  0
K  U el  0 (no external forces)
V1 < V2
Moving in the direction of E means that potential is decreasing
46
Sign of the Potential Difference
U el  qV
To move a positive charge to the
area with higher potential:
Vf – Vi > 0
U el  qV  0
Need external force to perform work
V1 < V2
Moving opposite to E means that potential is increasing
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