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QuickCheck 29.7
A particle follows the trajectory
shown from initial position i to
final position f. The potential
difference V is
A.
B.
C.
D.
E.
100 V.
50 V.
0 V.
50 V.
100 V.
Slide 29-54
QuickCheck 29.7
A particle follows the trajectory
shown from initial position i to
final position f. The potential
difference ΔV is
A.
B.
C.
D.
E.
100 V.
50 V.
0 V.
50 V.
100 V.
V = Vfinal – Vinitial, independent of the path
Slide 29-55
Questions
•
•
•
•
How can we create an electric potential?
How can we relate V to E geometrically? Mathematically?
Fundamentally what creates a potential difference?
What are different ways we use energy to generate a potential difference?
How to create an electric potential
difference (voltage)?
• Mechanically
• Chemically
• Electromagnetically
How to create an electric potential
difference?
• Mechanically
• Chemically
• Electromagnetically
Mechanically
Van de Graaff generator
Chemically
• Electrodes and electrolytes
https://www.youtube.com/watch?v=0TvYlJ06MXo
https://www.youtube.com/watch?v=HhxtfULIO7c
Chemically
Chemically
Batteries and emf
• Electromagnetically
Charged capacitor
Which electric potential graph
describes this electric field?
A.
B.
C.
D.
E.
Which electric potential graph
describes this electric field?
*Flip graph about the horizontal axis.
Potential, potential energy, force,
electric field

FC
UC


FC  qE

E
U C  qV
V
One dimension – two examples
dV
V   Ex  E  
dx
The component of E along the path travelled
contributes to the change in electric potential along
the path.
Potential and field
2
 
V2  V1    E  dr
1
Potential and field
dV
V   Ex  E  
dx
Which set of
equipotential surfaces
matches this electric
field?
1
2
4
3
5
21
Which set of equipotential
surfaces matches this electric
field?
1
2
4
3
5
22
Which E-vector is correct??
A
B
C
0V
-10V
D
-20V
-30V
Which E-vector is correct??
A
B
C
0V
-10V
D
-20V
-30V
Potential and field
2
 
V2  V1    E  dr
1


V ˆ V ˆ V ˆ
E  V  
i
j
k
x
y
z
Rank the electric field magnitudes
from largest to smallest.
Rules for field and equipotential lines
• Electric field lines and equipotential lines are
always perpendicular to each other
• Equipotential lines NEVER cross
• Electric field points in direction of decreasing
potential
• Denser equipotential lines (or electric field lines)
=> stronger electric field
Potential in a conductor
A)Va>0
B)Va=0
C)Va<0
D)Insufficient info
Va
V=0
Potential in a conductor
A)Va>0
B)Va=0
C)Va<0
D)Insufficient info
Va
V=0
E vs V
• What is the electric potential at point (x,y,z) when and the potential at point
(2,2,1) is 10V?
Not enough information!
E and V
• OK, technically, this equation above isn't actually a
conservative field, but the technique is correct. If you
took a different path you would actually get a
different answer. This would be a better example:
E (r )=xy 2 x^ + y (3+x 2 ) y^ +5 z ^z
*In Class notes – see next page for full solution.
Potential and Field
2
2
2
If we have V(x,y,z)=x +y +z , then the electric field is
(A) 
E =−2 x−2 y −2 z
(B) 
E =−2 r
(C) 
E =0
(D) 
E =−2
Potential and Field
2
2
2
If we have V(x,y,z)=x +y +z , then the electric field is
(A) 
E =−2 x−2 y −2 z
(B) 
E =−2 r
(C) 
E =0
(D) 
E =−2
Potential due to a ring
Q
R
x=0
xP
1
V
4 0
Q
x R
2
P
2
End of Wednesday