Electric currents

1
Electric currents Electromagnetism

• Micro-world Macro-world
• Lecture 9

2
Electric currents
(Motion of electric charges)

• Micro-world Macro-world
• Lecture 9

3
Alessandro Volta
4
Positive Ions
Atoms with one or more electrons removed
_
_



_
_
_


_
_
_
net charge 2qe
5
Battery
C
Zn
Zn
- -

Zn
Zn
- -
Zn
Zn
- -
Zn
Zn

- -
Zn
- -
Zn
Zn
Zn

acid
6
Voltage
Cathode
Anode
-

-
-

-
-

-
E
-

-
Zn
-
F

W Fd
Voltage
d
F 2qeE
W0 2qe
V
W 2qeEd
? W0 2qeE0d
? E0d
7

Energy gained by the charge
W Fd
Q E0d
QV
FQE0
FQE0
Q
Q
Anode
-

Cathode
-
E0
-

-
-

Zn
-
-

-
Zn
-

d
8
Units again!
W Q V
joules
joules coulomb
W Q
?
V
Volt
coulombs
joule coulomb
1 V 1
9
Continuous charge flow electric current
Electrical conductor connected between anode
cathode
Q
Q
Anode
-

Cathode
-
-

-
-

Zn
-
-

-
Zn
-

10
electric current
Coulombs second
Units
Q t
I
Amperes
Q
Q
Anode
-

Cathode
-
-

-
-

Zn
-
-

-
Zn
-

11
The conductor can be a piece of wire
Q t
I



Anode
-

Cathode
-
-

-
-

Zn
-
-

-
Zn
-

12
The energy can be used to run a gadget
Energy time
QV t
P

I V

I


I
I
Anode
-

Cathode
-
-

-
-

Zn
-
-

-
Zn
-

13
Electric light
60 Watts I? T
Power P I V
P V
60 W 100V
I

J/s J/C
1/s 1/C
0.6
0.6
C s
V100V
0.6
0.6 A
14
General circuit
I
Appliance
-

I

-
12V
Energy source (device that separates - charge)
15
analogy
Amt of water flow current
appliance
Height voltage
Pump battery
pump
pond
16
Voltas 1st batteries
17
Christian Oersted
18
Electric currents produce B-fields
B
I
19
Right-hand rule
B
20
Current loop
N
S
21
Two current loops
N
S
22
Even more loops
S
N
23
Solenoid coil
S
N
Looks like a bar magnet
24
Atomic magnetism
B

I
-
Some atoms are little magnets
25
Permanent magnet-microscopic view-
26
Magnetic forces on electric currents
I
27
Another right-hand rule
I
28
Forces on two parallel wires
I
I
Current in same direction wires attract
B
29
Forces on two parallel wires
I
Current in opposite directions wires repel
B
I
30
Force law of Biot Savart
I2
I1
I1I2 l d
F k
l
N A2
k 2 x 10-7
B
d
31
Biot Savart example
I1I2 l d
20A
20A
F k
(20A)2 2m 0.01m
N A2
F 2 x 10-7
2m
B
F 2 x 10-3N
Small, but not tiny
0.01m
32
Electric motor
F
I
I
B
F
33
Electric motor
B
I
34
Speakers
Solenoid Electro-magnet
Permanent magnet
35
Lorentz force
B
v
F
q
iqv
if v ? B
F iB qvB
direction by the right-hand rule
36
Electromagnetism
Michael Faraday
Faradays Law
37
Moving a Conductor in a B-fieldseparates -
charges
I
38
Use this to drive an electric circuit




I

39
Moving wire loop in a B field
v


An electric current is induced in the loop
40
Either the magnet or the loop can move
v


an electric current is induced in the loop
41
Magnetic flux (F) thru a loop
F BA-
42
Flux thru a coil of N loops
F N BA-
43
Faradays law
Michael Faraday
change in F elapsed time
Induced voltage in a circuit
change in N BA- elapsed time
EMF
Electro-Motive Force
44
Rotating coil in B field
B
A- 0 ? F 0
45
Rotating coil in B field
B
A- Acoil ? F maximum
46
Rotating coil in B field
B
A- 0 (again) ? F 0
47
AC voltage
48
Lenz Law
B
B
S
B-field from induced current


B-field from induced current
I
N
v
v
the fall produces an induced current
the B-field produced by the induced current tries
to impede the fall
49
Lenz law

• An induced voltage always gives rise to an
  electric current that creates a magnetic field
  that opposes the influence that produced it.

50
Maglev trains
51
Maglev
52
Maxwells Equations
James Clerk Maxwell
and then there was light.
53
Properties of E B fields

• Coulombs law E-field lines start on charge
  end on charge
• Amperes law B-fields are produced by electric
  currents
• Faradays law Changing B-fields produce E-fields
• (un-named law) B-field lines never end

54
In equation form
E-field lines start on charges end on - charges
B-field lines never end
E-fields are produced by changing B fields
B-fields are produced by electric currents
55
Maxwell

• The previous equations, as written, are
  mathematically inconsistent with the conservation
  of electric charge. He found he could fix this
  by adding one more term

B-fields are produced by changing E-fields
56
Maxwells equations
B-fields are produced by changing E-fields
57
Fields from an electric charge
E
E
x
Is the change in E instantaneous? Does it occur
only after some time? M.E.s can tell us?


58
fun in the bathtub
Water level will increase
but not instantaneously
1st waves will propagate from her entrance
point to the edge of the tub
59
According to Maxwells eqs
E
E

x
The change in E is not instantaneous 1st waves
made of E-fields B-fields propagate thru space.


60
Wave solutions to Maxwells Eqs
?
k ?strength of electric force
2kk
Wave speed
q1q2 r2
Fc k
?
2x9x109Nm2/C2 2x10-7N/A2

k 9.0 x 109 Nm2/C2
?
k ?strength of magnetic force
9x1097(m2/C2)xA2

?
9x1016m2/s2

Speed of light!!
I1I2 l d
FM k
3x108m/s
N A2
k 2 x 10-7

61
let there be light.

• Maxwells equations have solutions that are waves
  of oscillating E- B-fields that travel at the
  speed of light.
• Faraday Maxwell made the immediate ( correct)
  inference that these waves are, in fact, light
  waves.

62
EM waves
-

-


-
63
antenna
E
B
64
antenna
E
B
65
Light wave
B-field

-
E-field
wave velocity
66
Light wave animation
E
B
67
Electro-magnetic spectrum
Infra- red
Ultra- violet
micro waves
radio waves
X-rays
g-rays
TV/FM
AM
Visible light l freq (c/l)
Red 0.75x10-6m 4.0x1014 Hz Green
0.55x10-6m 5.5x1014 Hz Violet
0.4x10-6m 7.5x1014 Hz