Electric currents& Electromagnetism
Micro-world Macro-worldLecture 9
Electric currents
Micro-world Macro-worldLecture 9
(Motion of electric charges)
Alessandro Volta
Positive Ions
_
_
_
_
++++
+
Atoms with one or moreelectrons removed
”net” charge = +2qe
_
_
_
_
Battery
C ZnZn
ZnZn
ZnZn++ - -
Zn++ - -
Zn++- -+ +
Zn++- -+ +
Zn
ZnZn - -+ +
acid
“Voltage”Anode
+ ++ +
+ +
Cathode
-
- - - - -
EZn++
F
+ ++
- - -
W = FddF = 2qeE
W = 2qeEd W0 = 2qeE0d =E0dW0 2qe V
“Voltage”
Anode
+ ++ +
+ +
Cathode
-
- - - - -
F=QE0
+ ++
- - -
W = Fd
E0
Q F=QE0Q
=Q E0d = QV
d
Zn++
Zn++
Energy gained by the charge
Units again!
W = Q V
V = W Q
joules
coulombs
joules coulomb
= Volt
1 V = 1 joule coulomb
Continuous charge flow = “electric current”
Anode
+ ++ +
+ +
Cathode
-
- - - - -
+ ++
- - -
Zn++
Zn++
Q Q
Electrical “conductor” connected between anode & cathode
electric current
Anode
+ ++ +
+ +
Cathode
-
- - - - -
+ ++
- - -
Zn++
Zn++
Q Q
I = Qt
Units:Coulombssecond
=Amperes
The conductor can be a piece of wire
Anode
+ ++ +
+ +
Cathode
-
- - - - -
+ ++
- - -
Zn++
Zn++
I = Qt
+ ++
The energy can be used to run a gadget
Anode
+ ++ +
+ +
Cathode
-
- - - - -
+ ++
- - -
Zn++
Zn++
P= Energy
time
+ ++
QVt= = I V
I I I
Electric light
60 Watts I=?
T
Power = P = I V
I = P V = 60 W
100V
= 0.6 J/s J/C = 0.6 1/s
1/C
= 0.6 C s = 0.6 AV=100V
General circuit
12V
+ -
Appliance+ -
Energy source(device that separates+ & - charge)
I
I
analogy
Height ~ voltage
Pump ~battery
Amt of water flow ~ current
appliance
pond
pump
Voltas’ 1st batteries
Christian Oersted
Electric currents produce B-fields
I
B
Right-hand rule
B
Current loop
NS
Two current loops
NS
Even more loops
NS
Solenoid coil
Looks like abar magnet
SN
Atomic magnetism
+- I
B
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
II
Current in samedirection:
wires attractB
Forces on two parallel wires
I
I
Current in oppositedirections:
wires repelB
Force law of Biot & Savart
I2I1
F =
B
I1I2 ld
l
d
= 2 x 10-7 NA2
Biot & Savart example
20A F =
B
I1I2 ld
2m
0.01m
F = 2 x 10-7 NA2
20A
(20A)2 2m0.01m
F = 2 x 10-3N
Small, but not tiny
Electric motor
IB
F
IF
Electric motor
I
B
Speakers
Permanentmagnet
SolenoidElectro-magnet
Lorentz force
B
+q
v
i=qv
F
F = iB = qvBif v B:
direction by the right-hand rule
Electromagnetism
Michael Faraday
Faraday’s Law
Moving a Conductor in a B-fieldseparates + & - 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 () thru a loop
= BA┴
Flux thru a coil of N loops
= N BA┴
Faraday’s law
change in N BA┴elapsed time
Induced voltage in a circuit = change in elapsed time
EMF =
“Electro-Motive Force”
Michael Faraday
Rotating coil in B field
A┴ = 0 =0
B
Rotating coil in B field
A┴ = Acoil = maximum
B
Rotating coil in B field
A┴ = 0 (again) = 0
B
AC voltage
Lenz’ Law
v v
B B
+ +N
S
the fall producesan induced current
the B-field producedby the induced currenttries to impede the fall
B-field from induced currentB-field from
induced currentI
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
+
xE
+
E
Is the change in Einstantaneous?
Does it occur onlyafter some time?
M.E.s can tell us?
fun in the bathtub
Water level will increase
but not instantaneously
1st waves will propagatefrom her entrance pointto the edge of the tub
According to Maxwell’s eqs:
+
xE
+
E
The change in Eis not instantaneous
1st waves made of E-fields & B-fields propagate thru space.
Wave solutions to Maxwell’s Eqs:
Fc = k q1q2
r2
k = 9.0 x 109 Nm2/C2
k ”strength” of electric force
FM = I1I2 ld
= 2 x 10-7NA2
”strength” of magnetic force
2k
Wave speed =
2x9x109Nm2/C2
2x10-7N/A2
=
9x109+7(m2/C2)xA2=
9x1016m2/s2=
= 3x108m/s Speed of lig
ht!!
“…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
-
+-+
+
-
antennaE
B
antenna
E
B
Light wave
E-field
B-field
wave velocity
+
-
Light wave animation
E
B
Electro-magnetic “spectrum”
Visible light: freq (c/)
Red 0.75x10-6m 4.0x1014 Hz
Green 0.55x10-6m 5.5x1014 Hz
Violet 0.4x10-6m 7.5x1014 Hz
Ultr
a-vi
olet
Infr
a-re
d
X- rays
- rays
mic
ro
wav
esra
dio
wav
es
TV/F
M
AM
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