Download Electromagnetic induction

Remember?
 An electron is moving downward with a velocity, v,
in a magnetic field directed within the page,
determine direction of force.
Moving conductor
 Conductors contain free electrons
 So when a conductor moves
downward, electron will experience a
magnetic force pulling them to the
left.
 Lattice atoms on the right become
positive…
 There is a potential difference now
Moving conductor
 E force produced wanting to push
electrons to the right
 Forces are now balanced and electrons
will stop moving
 What will happen if you connect a
resistor to the metal conductor?
Moving conductor
R
 E force produced wanting to push
electrons to the right
 Forces are now balanced and electrons
will stop moving
 What will happen if you connect a
resistor to the metal conductor?
 Current will flow from high to low
potential
–
–
–
+
+
+
Moving conductor
R
 What did we define emf previously as?
 Amount of chemical energy converted
to electrical energy per unit charge
–
–
–
+
+
+
Moving conductor
R
 What did we define emf previously as?
 Amount of chemical energy converted
to electrical energy per unit charge
 We don’t have chemical energy here!!!
 Where does our energy come from
here?
–
–
–
+
+
+
Moving conductor
R
 Which direction were we pushing this
conductor?
 Another force acting on conductor?
–
–
–
+
+
+
Moving conductor
R
 Which direction were we pushing this
conductor?
 Another force acting on conductor?
 Yes magnetic force… which direction
is it acting?
–
–
–
+
+
+
Moving conductor
Magnetic force
R
 Which direction were we pushing this
conductor?
–
–
–
+
+
+
 Another force acting on conductor?
 Yes magnetic force… which direction
is it acting? – upward
 So when you’re pushing it downward,
what energy is it gaining?
Force applied
Moving conductor
 Which direction were we pushing this
conductor?
 Another force acting on conductor?
Magnetic force
R
–
–
–
+
+
+
 Yes magnetic force… which direction
is it acting? – upward
 So when you’re pushing it downward,
what energy is it gaining? – EPE
 You are doing work
 If forces are equal, conductor is
moving at constant v.
Force applied
Moving conductor
Magnetic force
R
 EPE will be converted into heat
 Energy is conserved
–
–
–
+
+
+
 Now let’s define INDUCED EMF?
 Amount of mechanical energy
converted into electrical energy per unit
charge.
Force applied
Calculating induced EMF
 Maximum p.d. in conductor is when the magnetic
force ON ELECTRON is equal to the electrical force
L
–
Calculating induced EMF
 Maximum p.d. in conductor is when the magnetic
force ON ELECTRON is equal to the electrical force
L
–
 Electron will stop moving.. Therefore greatest p.d.
 Equate equations
Induced EMF equation
*
*
FB = FE
Vq
= Bvq
L
V = BLv
The induced EMF will be the same as
p.d. across conductor
Question
 If magnetic field not perpendicular to direction of
motion… what will you do?
B
v
q
Question
 If magnetic field not perpendicular to direction of
motion… what will you do?
e = Bsinq vL
OR
e = B cosq vL
 Take the B that is perpendicular to v
QUESTION
QUESTION
ield of current
the magnetic field is perpendicular to the
e direction the fingers of your right hand
u wrapped them around the wire with your
ection of the current.
THREE HAND RULES
RIGHT
LEFT
Faraday’s law
 What generated induced emf?
 What did it depend on?
Faraday’s law
 What generated induced emf? – moving conductor
in a magnetic field
 What did it depend on?
 Faraday’s law:
 The induced emf is equal to the rate of change of flux
Flux VS flux density
 Let’s look at this analogy
Flux VS flux density
 How much grass do you have?
 Is it taking lots of area?
Flux VS flux density
 Pieces of grass is flux density (B)
 Area over which grass takes over is flux (Φ)
Flux VS flux density
F = BA
Flux unit: Tm2, Wb
Flux VS flux density
 If area at angle from B
 Find component of B that will be perpendicular to
area
Normal to surface
θ
Lenz’s law
 Moving conductor in magnetic field causes a force to
oppose the direction of motion as seen earlier (if not
true than energy will not be conserved)
 Lenz’s law is an extension to Faraday by stating that:
 the induced current will be in such a direction as to
OPPOSE THE CHANGE IN FLUX that created the
current.
Question
Question
Question
 Determine direction of current
Question
Question
Question
Question
Question
 Rail gun… how does it work?
resistor
Question
 What will happen if you remove the magnetic field
suddenly?
resistor
Question
 BRING BACK THE FIIIEEEELLLDDD!!! LENZ’S LAW
resistor
Question
 to get the field back, which direction should the
induced current be?
resistor
Question
 Current upward…. Force????
resistor
Question
 Current upward…. Force to the right… and off it
goes…..
resistor
Question
Question
http://science.howstuffworks.com/rail-gun1.htm
Read
 Applications of EM induction on page 213
Alternating current (AC)
 What’s the difference between a motor and a
generator?
Alternating current (AC)
 What’s the difference between a motor and a
generator?
 Motor  electrical to mechanical energy
 Generator  mechanical to electrical
Alternating current (AC)
 What’s the direction of current induced here?
Alternating current (AC)
 What’s the flux going to be at angle 0?
Alternating current (AC)
 What’s the flux going to be at angle 0?
 Maximum since
 So how will the graph look like?
Alternating current (AC)
Label the positions in graph
Alternating current
 Since we have many loops here we change the
equation a bit and add “N” so that the total flux
(called flux linkage):
flux linkage = NF
flux linkage = NBAcosq
 Can we substitute θ with something else?
Alternating current
 .
flux linkage = NBAcos(wt)
Alternating current (AC)
 How will the emf graph with time look like?
 What’s the emf equation?
Alternating current (AC)
 How will the emf graph with time look like?
 What’s the emf equation?
 How can we get this value from the flux vs time
graph?
Alternating current (AC)
 How will the emf graph with time look like?
 What’s the emf equation?
 How can we get this value from the flux vs time
graph? ---- (negative the gradient)
Alternating current (AC)
Alternating current (AC)
 So will the equation for emf have a sin or cos?
Alternating current (AC)
 So will the equation for emf have a sin or cos?
e = NBAw sin(wt)
 Therefore at 90 degrees the emf in max and the flux
is zero.
Alternating current (AC)
Emf and time
 Emf vs time graph… what will happen if you double
the angular speed…
Emf and time
 Emf vs time graph… what will happen if you double
the angular speed…
 Double emf and half the period
Current and time
 How can the current in the circuit be found?
Current and time
 How can the current in the circuit be found?
I=
I=
e
R
e 0 sin(wt)
R
I = I0 sin(wt)
 ε0 is equal to:
e 0 = NBAw
 Can you think from where this equation came from?
Graphs
Definitions
 AC: current delivered by rotating coil changing in
direction and size over period of time
 DC: constant current delivered from battery
question
Answer
Power
 Equation(s)?
Power
 P=IV, let substitute…
P = eI = (e 0 sin(wt))(I0 sin(wt)) = e 0 I0 sin (wt)
2
 always positive
Power
 Average power is about 50W in example below…
how about the average current and voltage from
previous graphs?
Power
 Average power is about 50W in example below…
how about the average current and voltage from
previous graphs?
 ZERO????
 How do we solve this?
RMS
 To solve this by calculating the root mean square
(rms)
 Square voltage or current then divide by two then
square root the answer
E rms =
Irms =
e
2
0
2
=
e0
2
I02
I0
=
2
2
Question
Question
Power loss
 Power transmitted through wire will be lost due to
what factors?
Power loss
 Power transmitted through wire will be lost due to what
factors?
 P=I2R [power loss to heating]
pl
R=
A
 To reduce heat loss we have to reduce I
 Reducing current, if DC was transmitted through power
lines that feed homes, will have nothing left to run
instruments..
 AC, on the other hand, keeps on changing current and
voltage…
Power loss
 P=IV
 So if we increased V then I will decrease since power supply in
constant
 So if we increase voltage by 100V, then the current will be
less (I /100)
 So the power loss will be reduced by 1002 (P=I2R)
 WOW very useful and can only happen in AC
 Ok… how can we do this? Transformers
Transformers
 NO! Not the movie :p
Transformer
iron
 Current runs through primary.. What will it generate?
Transformer
iron
 Current runs through primary.. What will it generate?
Transformer
iron
 Current runs through primary.. What will it generate?
 A magnetic field will be generated in all iron (that’s
why it has to be a magnetic metal)
 Now there is a magnetic field in in secondary coil..
What will happen?
Transformer
iron
 Current runs through primary.. What will it generate?
 A magnetic field will be generated in all iron (that’s
why it has to be a magnetic metal)
 Now there is a magnetic field in in secondary coil..
What will happen? NOTHING
 How can we make a current run through the
secondary coil?
Transformer
iron
 Current runs through primary.. What will it generate?
 A magnetic field will be generated in all iron (that’s
why it has to be a magnetic metal)
 Now there is a magnetic field in in secondary coil..
What will happen? NOTHING
 How can we make a current run through the
secondary coil? CHANGE THE FLUX – INDUCED EMF
Transformer
iron
 CHANGE IN FLUX created a current
 Potential difference in primary coil is proportional to
number of loops
V µN
 so
Transformer
iron
 So lets look at the example above
 Number of loops in secondary is greater than
primary
 So voltage in secondary will also be larger than
primary
 So how about the current?
Transformer
iron
 Look at above equation
 Since voltage is more than the current will be less
(since the power is constant).
 So we just have MORE VOLTAGE (10/5 so double
voltage) :D Step up transformer
Transformer
iron
 Step up transformer to transport from plant to
houses
 Step down transformer at home to devices
Transformer
Question
answer
answer
Read
 For more information 218 and 219