Short Version : 22. Electric Potential
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Electricity Potential - General Physcis - Lecture Slides, Slides of Physics
Physics is about nature. This course covers almost every concept related to physics. Important points in this lecture are: Electric Potential, Electric Potential Difference, Force, Field, Potential Energy, Path Independent, Charged Sheet, Calculating Potential Difference, the Zero of Potential, Science Museum
Typology: Slides
2012/2013
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Short Version :
22. Electric Potential
22.1. Electric Potential Difference
Conservative force:
AB
B^
A
U
U
U
AB W
B A^
d
F
r
Electric potential difference
electric potential energy difference per unit charge B A^
d
E
r
AB
AB
U
V
q
B V
if reference potential V
A
= 0.
[ V ] = J/C = Volt = V
For a uniform field:
AB
AB
V
E r
^
B^
A
^
E
r
r
( path independent )
r
AB
E Docsity.com
Potential Difference is Path Independent
Potential difference
V
AB
depends only on positions of
A
&
B
.
Calculating along any paths (1, 2, or 3) gives
V
AB
=
E
r.
Example 22.2.
Charged Sheet
An isolated, infinite charged sheet carries a uniform surface charge density
.
Find an expression for the potential difference from the sheet to a point aperpendicular distance
x
from the sheet.
^
0
x V
E
x
0 2
x
^
E
The Zero of Potential
Only potential differences have physical significance.
Simplified notation:
RA
A^
R^
A
V
V
V
V
R = point of zero potential
V
A
= potential at
A
.
Some choices of zero potential
Power systems / Circuits
Earth ( Ground )
Automobile electric systems
Car’s body
Isolated charges
Infinity
Example 22.3.
Science Museum
The Hall of Electricity at the Boston Museum of Science contains a large Van de Graaff generator, a devicethat builds up charge on a metal sphere.The sphere has radius
R
= 2.30 m and develops a charge
Q
= 640
C.
Considering this to be a single isolate sphere, find(a) the potential at its surface,(b) the work needed to bring a proton from infinity to the sphere’s surface,(c) the potential difference between the sphere’s surface & a point 2
R
from its center.
^
^
Q
V
R
k
R
^
^
6
9
/^
C
Vm
C
m
(a)
M
V
^
W
e V
R
(b)
M
eV
^
19
C
MV
13
J
^
^
^
,
R^
R
V
V
R
V
R
(c)
Q 2
Q
k
k
R
R
Q 2
k
R
M
V
Finding Potential Differences Using Superposition
Potential of a set of point charges:
^
^
i
i^
P^
i
q
V
P
k
r
r
Potential of a set of charge sources:
^
^
^
i
i
V
P
V
P
Example 22.5.
Dipole Potential
An electric dipole consists of point charges
q
a distance 2
a
apart.
Find the potential at an arbitrary point
P
, and approximate for the casewhere
the distance to
P
is large compared with the charge separation.
^
^
^
1
q 2
q
V
P
k
k
r
r
1
2
kq
r^
r
^
^
^
2
2
2
1
cos
r^
r^
a
r a
2
2
2
2
cos
r^
r^
a
r a
2
2
2
1
cos
r
r^
r a
^
2
1
1
2
r^
r
r^
r
r^
a
2
1
cos
r^
r^
a
^
^
2
1 2 r
r
V
P
k q
r
2
cos
qa
k
r
2 cos p k
r
p
= 2
qa
= dipole moment
2
1
2
1
r^
r
kq
r r
+q: hill
q: hole
V = 0
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Example 22.6.
Charged Ring
A total charge
Q
is distributed uniformly around a thin ring of radius
a
.
Find the potential on the ring’s axis.
^
^
dq
V
x
k
r
2
2
k
dq
x
a
2
2
k
Q
x
a
Same
r
for all
dq
Q
k
x
a
x
Example 22.7.
Charged Disk
A charged disk of radius
a
carries a charge
Q
distributed uniformly over its surface.
Find the potential at a point
P
on the disk axis, a distance
x
from the disk.
^
V
x
dV
2
2
k
dq
x
r
^
2
2
2 2
k Q
x
a
x
a
2
2
0
a^
k
Q
r dr
a
x
r
2
2
2
0
a
Q
r
k
dr
a
x
r
2
2
2
0
a
Q
k
x
r
a
sheet
point charge
disk
^
2
0
k Q
kQ
a
x
x
x
a
a
a
k Q
x
a
x
Calculating Field from Potential
r^ B A
AB
r
V
d
E
r
dV
d
E
r
i^
i
i
E dx
i
i^
i V
d x x
i
i V
E
x
V
E
=
( Gradient of V )
V
V
V
x
y
z
E
i^
j^
k
E
is strong where V changes rapidly ( equipotentials dense ).
Example 22.8.
Charged Disk
Use the result of Example 22.7 to find
E
on the axis of a charged disk.
Example 22.7:
^
^
^
2
2
2 2
k Q
V
x
x
a
x
a
2
2
2
k Q
x
a
x
a
x
V
E
x
x > 0x < 0
y^
z
E
E
dangerous conclusion
22.4. Charged Conductors
In electrostatic equilibrium,
E
= 0
inside a conductor.
E
//^
= 0
on surface of conductor.
W = 0 for moving charges on / inside conductor.
The entire conductor is an equipotential.
Consider an isolated, spherical conductor of radius
R
and charge
Q
.
Q
is uniformly distributed on the surface
E
outside is that of a point charge
Q
.
V
( r
) =
k Q
/
R
.^
for
r
R
.
Consider 2 widely separated, charged conducting spheres.
1
1
1 Q
V
k
R
2
2
2 Q
V
k
R
Their potentials are
If we connect them with a thin wire,there’ll be charge transfer until
V
1
=
V
2
, i.e.,
1
2
1
2
Q
Q
R
R
^
2
j
j
j
Q
R
In terms of the surface charge densities
1
1
2
2
R
R
we have
Smaller sphere has higher field at surface.
1
1
2
2
E
R
E
R
Same V
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