Transcript Electric currents - University of Hawaii

Electric currents
& Electromagnetism
Micro-world Macro-world
Lecture 9
Electric currents
Micro-world Macro-world
Lecture 9
Alessandro Volta
Positive Ions
Atoms with one or more
electrons removed
_
_
_
_
_
+
++
++
_
”net” charge = +2qe
_
_
Battery
C
Zn
Zn++
Zn
++
Zn
Zn
acid
Zn++
Zn++
Zn
Zn
-Zn
-Zn
-Zn
-
“Voltage”
Cathode
Anode
E
Zn++
W = Fd
F = 2qeE
F
--
d
W = 2qeEd  W0 = 2qeE0d

W0
=E0d
2qe
V
W = Fd =Q E0d = QV
Anode
Q
F=QE0
E0
Zn++
Zn++
d
Q
F=QE0
--
Cathode
Units again!
W=QV
W
V=
Q
joules
 coulomb
= Volt
joule
1 V = 1 coulomb
Continuous charge flow
= “electric current”
Anode
Q
Q
Zn++
Zn++
--
Cathode
electric current
Q
I=
t
Anode
Q
Coulombs
Units:
second
=Amperes
Q
Zn++
Zn++
--
Cathode
The conductor can be a piece of wire
Q
I=
t
+
+
Anode
Zn++
Zn++
+
--
Cathode
The energy can be used to run a
gadget
Energy
QV
P= time =
=IV
t
I
+
+
I
+
I
Anode
Zn++
Zn++
--
Cathode
Electric light
60 Watts
I=?
T
Power = P = I V
P
I=
V
=
60 W
100V
J/s
1/s
= 0.6
= 0.6
J/C
1/C
V=100V
C
= 0.6
s
= 0.6 A
General circuit
I
+ Appliance
+
-
12V
I
Energy source
(device that separates
+ & - charge)
Amt of water flow ~ current
analogy
appliance
Height ~ voltage
Pump ~
battery
pump
pond
Voltas’ 1st batteries
Christian Oersted
Electric currents produce B-fields
B
I
Right-hand rule
B
Current loop
S
N
Two current loops
S
N
Even more loops
S
N
Solenoid coil
S
Looks like a
bar magnet
N
Atomic magnetism
B
+
-
I
Some atoms are little magnets
Permanent magnet
-microscopic view-
Magnetic forces on electric currents
I
Another right-hand rule
I
Forces on two parallel wires
I
I
B
Current in same
direction:
wires attract
Forces on two parallel wires
I
B
I
Current in opposite
directions:
wires repel
Force law of Biot & Savart
I1
I2
I1I2 l
F=k
d
l
B
d
k = 2 x10-7
N
A2
Biot & Savart example
20A
I1I2 l
F=k
d
20A
F = 2x10-7
2m
B
N (20A)2 2m
A2 0.01m
F = 2 x 10-3N
Small, but not tiny
0.01m
Electric motor
F
I
I
B
F
Electric motor
B
I
Speakers
Solenoid
Electromagnet
Permanent
magnet
Lorentz force
B
v
F
if v  B:
i=qv
F = iB = qvB
direction by the right-hand rule
Electromagnetism
Michael
Faraday
Faraday’s Law
Moving a Conductor in a B-field
separates + & - charges
I
Use this to drive an electric circuit
+
+
+
+
I
+
Moving wire loop in a B field
v
+
+
An electric current is
“induced” in the loop
Either the magnet or the loop can
move
v
+
+
an electric current is
“induced” in the loop
Magnetic flux (F) thru a loop
F = BA┴
Flux thru a coil of N loops
F = N BA┴
Faraday’s law
Michael
Faraday
Induced voltage in a circuit =
EMF =
change in F
elapsed time
change in N BA┴
elapsed time
“Electro-Motive Force”
Rotating coil in B field
B
A┴ = 0  F =0
Rotating coil in B field
B
A┴ = Acoil  F = maximum
Rotating coil in B field
B
A┴ = 0 (again)  F = 0
AC voltage
Lenz’ Law
B
B
S
B-field from
induced current
+
v
the fall produces
an induced current
B-field from
induced current
+
I
N
v
the B-field produced
by the induced curre
tries to impede the fa
Lenz’ law
An induced voltage always gives rise to an
electric current that creates a magnetic
field that opposes the influence that
produced it.
Maglev trains
Maglev
Maxwell’s Equations
James Clerk Maxwell
“…and then there was light.”
Properties of E & B fields
• Coulomb’s law: E-field lines start on
+ charge & end on – charge
• Ampere’s law: B-fields are produced
by electric currents
• Faraday’s law: Changing B-fields
produce E-fields
• (un-named law): B-field lines never end
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
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
Maxwell’s equations
B-fields are produced by
changing E-fields
Fields from an electric charge
E
x
E
Is the change in E
instantaneous?
Does it occur only
after some time?
+
M.E.s can tell us?
+
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
According to Maxwell’s eqs:
E
x
E
The change in E
is not instantaneous
1st waves made of Efields & B-fields
propagate thru space.
+
+
Wave solutions to Maxwell’s Eqs:

Wave speed =
=

2x9x109Nm2/
C2
-7N/A2
2x109+7
9x10 (m2/C2)xA2

=  9x10
=
2k
k
16m2/s2
= 3x108m/s
k ”strength” of
electric force
q1q2
k r2
Fc =
k = 9.0 x 109 Nm2/C2
k ”strength” of
magnetic force
FM = k
k=2x
I 1I 2 l
d
10-7
N
A2
“…let there be light.”
Maxwell’s 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.
EM waves
+
+
+
-
antenna
E
B
antenna
E
B
Light wave
B-field
+
E-field
wave velocity
Light wave animation
E
B
l
freq (c/l)
0.75x10-6m
0.55x10-6m
0.4x10-6m
4.0x1014 Hz
5.5x1014 Hz
7.5x1014 Hz
Visible light:
Red
Green
Violet
red
Ultraviolet
Xrays
grays
TV/FM
AM
radio
wave
s
micro
wave
sInfra-
Electro-magnetic “spectrum”