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+ + + + + + + + + + + +
- - - - - - - - - - - -
+qfree on inner surface
-qfree on inner surface
Interior points electric field must be zero
-qbound
+qbound
E
D
P
0
1( )E D P
Symmetry – fields must be uniform – field lines perpendicular to plates
conductor dielectric+
+
+
+ +
-
-
-
0E
E
freebound
Gauss’s Law
0
free boundE
frequency
dielectricconstant
+ + + + + + + + + + + +
- - - - - - - - - - - -V = 0
BFe HFe
Bgap Hgap
Bair Hair
i
coil windings
gap region
iron core
r
XXXXXX
.
.
.
.
.
.
.
.1 2
34
Circulation loop: square of length L
Cross-section through electromagnet
B H M
Current iout of page
Current iinto page
B
width L
thickness t
area
Aq = - e
electrons are the chargecarriers in copper
0r A
d
0r A
d
E
+ - + - + - + -
+ - + - + - + -
+ - + - + - + -
+ - + - + - + -
b b
+ + + + + + + + +
+ + + + + + + + +
- - - - - - - - -
dy
F
+q -q
d
+ + + + + + + + +
- - - - - - - - -
x
L-x
V r
C = CA + CB
Induced dipole moment – helium atom
-e -e+2e
Zero electric field – helium atom symmetric zero dipole moment
-e +2e -e
E
d
A B
effectively charge +2e at A and -2e at B
dipole moment p = 2 e d
p
Induced dipole moment – sulfur atom
-8e -8e+16e
Zero electric field – helium atom symmetric zero dipole moment
-8e +16e -8e
E
d
A B
effectively charge +16e at A and -16e at B
dipole moment p = 16 e d
p
-q +qd
r1 r – (d/2)cos
r2 r + (d/2)cos
r
P
ErE
(d/2)cos
+ + + + + + + + +
- - - - - - - - -
+f
-f
dA
-b
+b
d
+q-q
+f
-b
+b
-f
O
r
S
P
-
dr
Pcos
S
--
+ + +
E
The area of the shaded ring between and + d is equal to
2 sinr d
sinr
ˆb P n
E
a
+Ze
ad
+Ze
d << a
E
F
F
F
d
+Q
- Q
p
0 π/2 π
0
+ p E
- p E
U
T
Po
p E / k T
1
0 10
oP
n p
slope = 1/3
non-conducting liquid
airconducting
sphere q
a
Gaussian surface S
r
Symmetry field lines must be radial
non-conducting liquid
airconducting
sphere q
Symmetry Eairt = Eliquidt Eair = Eliquid = E
Eairt
Eliquidt
field lines of E field lines of D
+ -
E
induced dipoles due to shift in electron cloud
+
+
-
rotation orientation of polar molecules
-+
shift in atoms due to ionic nature of bond
NS
1 2 3
4
HFe Hair0
airFe
BH
2 3 5 6
1 2 4 5
2 6 3 5
1 5 2 4
0Fe air air Fe
Fe Fe air air
Fe air
H dl H dl H dl H dl H dl
H dl H dl H dl H dl
H H
Circulation loop: square side L
56
outsideB
insideBoutsideA
insideA
0inside outside
inside outside
B dA B A B A
B B
B-field lines – form continuous loops
Gauss’s Law for magnetism Cylindrical Gaussian surface
H
M
0M B
H
Bound surface currents (right hand screw rule) M
B
N pole
un-magnetized piece of iron
N
Bar magnet bought near un-magnetized piece of iron
B
N N
Bar magnet will attract the iron that was initially un-magnetizednorth pole attracts
south pole
Fe ramp Cu ramp plastic ramp
N N N
Circulation loop for circulation integration used in applying Ampere’s Law
N
N
Hiron
Hair
d
if
if
