Lecture 18
Superconductivity (100 years since the discovery)
will be presented by Professor Ruslan Prozorov
lecture slides will be posted at
http:/course.physastro.iastate.edu/phys222/Lectures%20(Prozorov)/Prozorov_18.pdf
Two questions:
(1) How to find the force, F on the electric charge, q excreted by the
field E and/or B?
F = qE + qv B
(2) How fields E and/or B can be created?
Maxwells equations
Gausss law for electric field
Electric charges create electric field:
E E
Lecture 14 will be presented by Professor Ruslan Prozorov
lecture slides can be found at
http:/course.physastro.iastate.edu/phys222/Lectures%20(Prozorov)/Prozorov_14.pdf
ConcepTest 20.8a Magnetic Field of a Wire I
Magnetic
1) direction 1
If the currents in these wires have
2) direction 2
the same magnitude, but opposite
3) direction 3
directions, what is the direction of
4) direction 4
the magnetic field at point P?
5) th
8. Magnetic field of moving charge
1) What is the problem with moving charge?
2) For v=0 and a=0:
(Coulombs law)
3) For
qr
E=k 2
rr
1
k=
4 0
v=0 and a=0:
(
)
1 v2 c2
( r r v c)
E = kq
( r r v c) 3
Speed of light:
4) For
B=0
(
c2 =
v<c and a=0:
0 qv r
B=
vd
A
n
N
lA
5. Magnetic forces on current
F = qv B
l
N nlA
lv d = l v d
F = Ftot = Nqvd B
= nlAqvd B
= nqAvd l B
F = Il B
nqAvd = I
- angle between vd and B
dF = Idl B
F = IlB sin
dF = IdlB sin
Example: A straight wire carrying a current is placed i
III. Magnetism
1. Electromagnetism in the laboratory and around us
2. Electromagnetism is simple. (If you know what it is!)
It is about:
q - electric charges
(magnetic charges do not exist)
F - electromagnetic forces
E - electric fields
B - magnetic field
Resistors in series and in parallel (review)
I
R1
V1
I = I1 = I 2
I1
R2
I
V2
V
I
I2
V = V1 + V2
I = I1 + I 2
Req = R1 + R2
Example
R1
= 12V
R1
R2
E
R2 = 30
12V
I=
=
= 0.26 A
R1 + R1 + r 47
V = V1 = V2
1
1
1
=
+
Req 15 30
Req = 10
r
Req = 15 + 30
R2
1
1
1
8. Power in electric circuits
I
R
V
W QV
P
=
= IV
t
t
W = QV
Q
=I
t
V = IR
2
V
P = IV = I R =
R
[ P] = 1W = 1V A = (1J / C ) (1C / s ) = 1J / s
2
Example: Two resistors, R1 = 5 , R2 = 10 , are connected in series.
The battery has voltage of V = 12 V.
a) F
6. Capacitance and capacitors
6.1 Capacitors
+Q
+Q
-Q
+Q
-Q
Symbol:
6.2 Capacitance
Definition:
Q
C=
V
Units:
[C]= 1 F = 1 C / V
V V V+ V
C is independent from: Q and V (V is always proportional to Q)
C depends on:
the geometry of the system
the dielectri
13. Comments about the induced electric field
(nonelectrostatic field)
For electrostatic field:
Edl = 0
When a charge goes around
a closed loop work is equal
to zero
W =0
Electrostatic field is conservative
Electric field lines do
not form closed loops
F
e = 1.60 10 19 C ; me = 9.11 10 31 kg
F =k
k=
V1 = V2 = . = V
Q1Q2
r2
1
= 8.99 10 9 N m 2 / C 2
4 0
0 = 8.85 10 12 C 2 / N m 2
Fnet = F1 + F2 + .
F = qE
E net = E1 + E 2 + .
_
E = d E = E cosdA = EdA
d
E
C eq = C1 + C 2 + .
= 4kQencl = Qencl 0
Q
4 0 r
12b. EMF induced in a moving conductor
A = lx = lvt
v
l
B
A
x = vt
B
BA
=
=
t
t
= Blv
1) What is polarity of EMF ?
2) What would be the direction of the induced
current, if rod slides on a conducting track ?
The B field points out of the page. The flux
19. LC circuits
Kirchhoffs loop rule:
C
v = q/C
L
ind
di
d 2q
= L = L 2
dt
dt
vC = ind
q
d 2q
= L 2
C
dt
d 2q
+ 2q = 0
dt 2
Solution:
d 2q
q
+
=0
2
LC
dt
=
1
LC
q = Q cos( t + )
i = Q sin ( t + )
vC = ( Q / C ) cos( t + )
Important: current and potent
22. AC current
1) General ideas
R
2
= 2f =
T
L
C
2) Phasor diagrams
V length of phasor
t
vR ( t ) ?
vC ( t ) ?
vL ( t ) ?
v( t ) = V cos t
V sin t
i( t ) ?
phasor
V cos t
23. AC circuits and reactance
1) Resistor
i ( t ) = I cos t
v( t ) = i ( t ) R = IR
24. LRC series circuit
1) Impedance
Current i(t) is the same in all
elements of the series circuit.
R
L
v( t )
Note! There is no current inside the capacitor,
but we can apply Kirchhoffs rules taking into
account displacement current
C
v R = VR cos t
i (
26. Electromagnetic waves
1) Maxwells equations and electromagnetic waves
2) Properties of electromagnetic waves
Speed of light:
1
c=
3 108 m / s
0 0
c
Wave length: =
f
Polarization of EM waves:
E
E
This wave is polarized in y direction
v
B
x
z
B
e.m. w
ConcepTest 22.2
ConcepTest
The electric field in an EM
wave traveling northeast
oscillates up and down. In
what plane does the
magnetic field oscillate?
Oscillations
Oscillations
1) In the north-south plane.
In
2) In the up-down plane.
In
3) In the NE-SW
7) Energy in electromagnetic waves
Energy density:
dU 1
B2
2
u=
= 0E +
dV 2
2 0
B = E/c
for e.m. wave
for any e.m. field
U B2
u= =
= 0E2
V 0
(U energy, V - volume)
Poynting vector:
Traveling EM waves transport energy. This energy transport can be describe
IV. Optics
Nature of light. Spectrum of electromagnetic waves.
Wavelength decreases
Frequency increases
Note: 1 nanometer = 10-9 meter
A. Geometric optics
1. Wave front and rays
rays
wave fronts
2. Reflection
in
normal to
surface
out
1 2
1 = 2
diffuse r
7. Spherical mirror
1) Mirror equation
C
do
h
h
h
h
< <1 ; ;
d0
di
R
= +
= +
+ = 2
di
if d i d o R 2 = f
if d o d i R 2 = f
Example:
112
+=
d0 di R
111
+=
d0 di f
R = 1.0m
121
2
1
5. 0
=
=
=
d i R d 0 1.0m 3.0m 3.0m
d o = 3. 0 m
di =
di ?
3.0
= 0.6m
Two questions:
(1) How to find the force, F on the electric charge, q excreted by the
field E and/or B?
F = qE + qv B
(2) How fields E and/or B can be created?
Maxwells equations
Gausss law for electric field
Electric charges create electric field:
E E