Transcript Faraday`s Law of Induction

Chapter 21
Electromagnetic Induction
and Faraday’s Law
A bit of review of Ch 20 …
There is a counterclockwise
current I in a circular loop of wire
situated in an external magnetic
field directed out of the page as
shown above. The effect of the
forces that act on this current is
to make the loop?
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1. expand in size
2. contract in size
3. rotate about an axis
perpendicular to the page
4. rotate about an axis in the
plane of the page
5. accelerate into the page
Which of the paths above
represents the path of an
electron traveling without any
loss of energy through a uniform
magnetic field directed into the
page?
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Induced EMF
Almost 200 years ago, Faraday looked for
evidence that a magnetic field would induce
an electric current with this apparatus:
Induced EMF
He found no evidence when the current was
steady, but did see a current induced when the
switch was turned on or off.
Induced EMF
Induced EMF: the potential difference created by a
changing magnetic field (flux) that causes a current to
flow in a wire.
The induced EMF in a wire loop is proportional to the
rate of change of magnetic flux (either the magnitude
of the field or the Area or both)through the loop.
Magnetic flux:
(21-1)
Unit of magnetic flux: weber, Wb.
1 Wb = 1 T·m2
Faraday’s Law of Induction
This drawing shows the variables in the flux
equation:
Magnetic Flux
The product of magnetic field and area.
Can be thought of as a total magnetic
“effect” on a coil of wire of a given area.
Maximum Flux
The area is aligned so that a
perpendicular to the area points parallel
to the field
Minimum Flux
The area is aligned so that a perpendicular
to the area points perpendicular to the field
Intermediate Flux
The area is neither perpendicular nor is
it parallel
Faraday’s Law of Induction
The magnetic flux is proportional to the total
number of lines passing through the loop.
Magnetic Flux
ΦB = B A cosθ
– ΦB: magnetic flux in Webers (Tesla
meters2)
– B: magnetic field in Tesla
– A: area in meters2.
– θ: the angle between the area and the
magnetic field.
ΦB = B·A
Sample Problem: Calculate the magnetic flux
through a rectangular wire frame 3.0 m long and
2.0 m wide if the magnetic field through the frame
is 4.2 mT.
a) Assume that the magnetic field is perpendicular
to the area vector.
b) Assume that the magnetic field is parallel to the
area vector.
c) Assume that the angle between the magnetic
field and the area vector is 30o.
Sample Problem: Assume the angle is
40o, the magnetic field is 50 mT, and the
flux is 250 mWb. What is the radius of
the loop?
Induced Electric Potential
• Armed with definition of flux, we can now look at
the induced current due to a changing magnetic
flux.
• A system will respond so as to oppose changes in
magnetic flux.
• A change in magnetic flux will be partially offset by
an induced magnetic field whenever possible.
• Changing the magnetic flux through a wire loop
causes current to flow in the loop.
• This is because changing magnetic flux induces an
electric potential.
Faraday’s Law of Induction
– Ɛ: induced potential (V)
– N: # loops
– ΦB: magnetic flux (Webers, Wb)
– t: time (s)
• To generate voltage, change B, change
A, change θ
An emf can be induced in one of three ways:
1) if the magnitude of the field changes
2) If the area of the loop changes:
3) If the angle between the loop face and the
direction of the field changes
Magnetic flux will change if the angle between
the loop and the field changes:
Sample Problem: A coil of radius 0.5 m
consisting of 1000 loops is placed in a 500 mT
magnetic field such that the flux is maximum. The
field then drops to zero in 10 ms. What is the
induced potential in the coil?
Sample Problem: A single coil of radius 0.25 m is
in a 100 mT magnetic field such that the flux is
maximum. At time t = 1.0 seconds, field increases
at a uniform rate so that at 11 seconds, it has a
value of 600 mT. At time t = 11 seconds, the field
stops increasing. What is the induced potential?
A) at t = 0.5 seconds?
B) at t = 3.0 seconds?
C) at t = 12 seconds?
Lenz’s Law
• Experiments show that the newly induced
current will flow in a direction so it’s
created magnetic field will try to oppose
the change in flux).
• Use in combination with hand rule to
predict current direction.
Problem Solving: Lenz’s Law
1. Point your right thumb in the initial direction of the magnetic field
2. Ask yourself, is the flux increasing or decreasing?
3. If the flux is decreasing, then just curl your fingers (with your
thumb still pointed in the direction of the magnetic field). Your
fingers show the direction of the induced current. (This is just the
RHR that you’ve already learned.)
4. If flux is increasing in the direction you’re pointing, then flux is
decreasing in the other direction. So point your thumb in the
opposite direction of the magnetic field, and curl your fingers. Your
fingers show the direction of the induced current.
5. Remember that the external field and the field due to the induced
current are different.
Sample Problem: The magnetic field is
increasing at a rate of 4.0 mT/s. What is the
direction of the current in the wire loop?
Sample Problem: The magnetic field is
increasing at a rate of 4.0 mT/s. What is
the direction of the current in the wire
loop?
Sample Problem: The magnetic field is
decreasing at a rate of 4.0 mT/s. The
radius of the loop is 3.0 m, and the
resistance is 4 Ω. What is the magnitude
and direction of the current?
Motional emf
Ɛ = BLv
– B: magnetic field (T)
– L: length of bar moving through field
– v: speed of bar moving through field.
• Bar must be “cutting through” field
lines. It cannot be moving parallel to
the field.
• This formula is easily derivable from
Faraday’s Law of Induction
Motional emf – derivation
Ɛ = ΔΦB / Δt
Ɛ = Δ(BA) / Δt (assume cosθ = 1)
Ɛ = Δ(BLx) / Δt
Ɛ = BL Δx / Δt
Ɛ = BLv
21.3 EMF Induced in a Moving Conductor
This image shows how the magnetic flux can
change in a rectangular wire:
ε = BLv
21.3 EMF Induced in a Moving Conductor
The induced current is in a direction that tends
to slow the moving bar – it will take an external
force to keep it moving.
Railgun
• http://www.military.com/video/guns/navalguns/railgun-update-from-generalatomics/904431955001/
• http://www.youtube.com/watch?v=y54aLc
C3G74&feature=related