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
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
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
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
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
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
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=
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
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
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
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
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
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) 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
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
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
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 (
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
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
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
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