Transcript Electromagnetic Induction

Electromagnetic
Induction
Electricity from Magnetism
Induced Current
When a conductor is moved in a
magnetic field, current can be induced
(caused)
Faraday’s Original Experiment
Many Ways to Produce EMF
Many forms of changing magnetic field can
produce Emf (current)
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Magnet or coil or both can move
Field can turn on or off due to closing or opening
a switch
Faraday’s Law (I)
Induced emf is proportional to the rate of
change of magnetic flux FB passing through
a loop of area A
FB = BAcosq
q is angle between
B and a line
perpendicular to
the face of the loop
Flux applet
Courtesy Dept. of EE Surrey University
Nature of Magnetic Flux
FB = BAcosq is a scalar
Above formula comes from “dot
product” of B and A whereas
F =Bqvsinq comes from “cross” or
vector product B x v
Unit of magnetic flux is tesla-meter2 or
weber
Ways of Changing Flux
Move coil into or out of field
Change area of coil
Rotate coil so number of field lines changes
Change field strength
Ways Flux will not change
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Rotate coil around field line – doesn’t change
number of field lines
Slide coil at constant angle within field
Faraday’s Law (II)
Magnetic flux is also proportional to total
number of field lines passing through loop
When q = 00 magnetic flux FB = BA (A is
area of loop perpendicular to magnetic field)
When q = 900 magnetic flux is zero; no field
lines pass through loop. Mathematically
Emf = -N D FB/ Dt
N is number of loops
Almost calculus
D FB/ Dt is time rate of
change of flux
Simple example
A square loop of side a enters a region
of uniform magnetic field B in time Dt =
one second. Write an expression for
the voltage induced during that interval
Emf =-N D FB/ Dt = -a2B/1 second =-a2B
Current direction?
How do we know in what direction,
clockwise or counterclockwise the
induced current will flow?
Energy conservation plays a role
Energy in the current and voltage must
come from somewhere
How this works is called Lenz’s Law
Lenz’s Law
Minus sign in Faraday’s Law reminds us that
An induced emf always gives rise to a current
whose magnetic field opposes the original
change in flux Applet
Induced current produces its own magnetic field
This field interacts with original field to make a force
Work must be done against this force to produce
induced current or conservation of energy will be
violated
How Current Varies
Link (demonstrates Lenz’s Law with bar
magnet and loop)
In Other Words
Physical motion that induces current
must be resisted by magnetic forces
Something has to do work to induce the
current, otherwise energy conservation
is violated
What is Direction of Current?
loop
Current clockwise
Field in this region
toward us
Changing Area – What is the
direction of induced current?
1. Field away from us xxx
2. Field toward us
. . .
Answer to 1. CW. Induced
field away to restore existing
field
Loop area shrinks
Answer to 2. CCW. Field
toward us to restore existing
field
What if Loop Area Increases?
Answers reverse
1 CCW
2 CW
Another Example of Lenz’s Law
When field is increasing, induced field
opposes it
When field is decreasing, induced field
acts in the same direction
Diagram courtesy Hyperphysics web site
Example: Square coil side 5.0 cm with
100 loops removed from 0.60T uniform
field in 0.10 sec. Find emf induced.
•Find how flux FB = BA changes during Dt = 0.10 sec.
•A = 2.5 x 10–3 m2
•Initial FB 1.5 x 10-3 Wb
•Final FB = zero
•Change in flux is -1.5 x 10-3 Wb
•Emf = -(100)(-1.5 x 10-3 Wb)/(0.10 s) = 1.5 volts
Example, continued
If resistance of coil is 100 ohms what are current, energy
dissipated, and average force required?
• I = emf/R = 1.5v/100 ohms = 15mA
•E = Pt = I2Rt= 2.25 x 10-3 J
• F = work required to pull coil out/distance = energy
dissipated in coil/distance = W/d = 0.050 N
Use d = 0.05 m since no flux change
until one edge leaves field
EMF in a Moving Conductor
Courtesy P Rubin, university of Richmond
Moving Rod Changes Area of Loop
•Let rod move to right at speed v
•Travels distance Dx = v Dt
•Area increases by DA = LDx=L v Dt
•By Faraday’s law
•Emf = D FB/ Dt = BDA/Dt =
BLvDt/Dt = BLv
•B, L and v must be mutually
perpendicular
Alternate Derivation of emf = BLv
•Force on electron in rod moving
perpendicular to magnetic field
strength B with speed v is F=qvB
acting downward
•Produces emf with top of rod +
•CCW conventional current as rod
slides to right
•Work to move a charge through
rod against potential difference is
W = Fd = qvBL. Emf is work per
unit charge BLv
Blv Example: Voltage across
an airplane wing
Airplane with 70 m wing travels 1000 km/hr through earth’s
field of 5 x 10-5 T. Find potential difference across wing. Is
this dangerous?
•Emf = Blv = (5.0 x 10-5 T) (70m) (280 m/s) = 1.0volt
•Could such a potential difference be used to reduce the
aircraft’s need for fuel?
The Generator
Generators and alternators work by rotating a
coil in a magnetic field. They produce
alternating current.