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LECTURE 7 slide 1
Lecture 7
Electrostatic Potential
Sections: 4.1, 4.2, 4.3, 4.4
Homework: D4.1, D4.2, D4.3, D4.4, D4.5; 4.3, 4.4, 4.5, 4.6,
4.9, 4.10, 4.12
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LECTURE 7 slide 2
Work 1
differential work
cosW dW d FdL = = =F L F L
work done fromA toB
, JB
W d= F L
work is positive if the applied force is in thedirection of displacement
work is negative if the applied force is opposite to the direction
of displacement
FL
0W F L = >
F L
0W F L =
cos 0, rock gains energyg gW F L =
L
gF
mF
0m mW F L= F L E L BextF
E Q=F E
displacem
ent
Q
+ + + + +
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LECTURE 7 slide 8
Work of Electric Field to Move Charges
if charge is already atB and is free to move, the electric field will
bring it back toA at the expense of its own energy (charge loses
potential energy WE)
0
A B
E E
B A
W Q d W Q d = = = > E L E L
A B
B Ad d = E L E L
B
displa
cementE Q=F E
+ + + + +
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LECTURE 7 slide 9
Electrostatic Potential Difference (Voltage)
Definition 1:potential difference VAB is the work done by the electric field in
moving a unit test charge from pointA to pointB
, VB
AB
A
V d= E L
Definition 2:
potential difference VAB is the work done by external forces in
moving a unit test charge from pointB to pointA
, VA
AB
B
V d= E L
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LECTURE 7 slide 10
Example: Potential Difference in the Field of Line Charge
Find the voltage VABbetween pointA(A,A,zA) and pointB(B,B,zB)in the field of a line charge l along thezaxis. Take the path along
the line segments: 1) , ,2) , ,
3) , ,
A A B A
B A B
B B B
z zz z z
z z
= == =
= =
00
( , , ) ( , , )
( , , )
B B
A AB
A
zB
AB A A A A B z
A z
B B
V d z d z dz
z d
= = + +
E L E a E a
E a
1
2
l
= E a
ln2
l BAB
A
V
= Can we choose B orA at infinity
or at zero?
note independence of angular position
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LECTURE 7 slide 11
Electrostatic Potential
Definition 1:the potential at a pointA is the work done by the electric field in
moving a unit test charge from pointA to a reference pointA0where the potential is assumed equal to zero
0
0
, V
A A
A
A A
V d d= =
E L E L
Definition 2:
the potential at a pointA is the work done by an external force in
moving a unit test charge from a reference pointA0, where the
potential is assumed equal to zero, to the pointA.
the electrostatic potential is the potential energy of a unit test
charge
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LECTURE 7 slide 12
Potential of a Point/Spherical Charge
1
4 AA
QV
=
N24A
A R RA R d
QV d dR
R
= =
LE L a a
assume potential is zero at infinity
integrate along any radial line
1
4
A
A
QV
=
+ A
E
the potential is the same for all points on the sphere of radius RA
we say that the sphere is an equipotential surface
notice the 1/R dependence on distance and compare it with E
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LECTURE 7 slide 13
You have learned:
how to compute work integrals
what potential difference (voltage) is in field theory
what we mean by a positive and a negative work
what absolute potential is
that the potential of a point/spherical charge depends on distance
as 1/R unlike E which decreases as 1/R2
what the potential difference is in the field of a line charge