induced emf is produced by a changing magnetic field
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Transcript induced emf is produced by a changing magnetic field
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“Never express yourself more clearly than you are able to think.”—Neils
Bohr
Chapter 21
Electromagnetic Induction
Faraday’s Law
ac Circuits
We found in chapter 20 that an electric current can give rise
to a magnetic field, and that a magnetic field can exert a force
on a moving charge.
I wonder if a magnetic field can somehow give rise to an
electric current…
21.1 Induced emf
It is observed experimentally that changes in magnetic fields
induce an emf in a conductor.
An electric current is induced if there is a closed circuit (e.g.,
loop of wire) in the changing magnetic field.
A constant magnetic field does not induce an emf—it takes a
changing magnetic field.
Passing the coil through the
magnet would induce an emf in
the coil.
They need to calibrate
their meter!
Note that “change” may or may not not require observable (to
you) motion.
A magnet may move through a loop of wire, or a
loop of wire may be moved through a magnetic field
(as suggested in the previous slide). These involve
observable motion.
http://hyperphysics.phy-astr.gsu.edu/
hbase/electric/farlaw2.html#c1
A changing current in a loop of wire gives rise to a
changing magnetic field (predicted by Ampere’s
law) which can induce a current in another nearby
loop of wire.
In the this case, nothing observable (to your eye) is moving,
although, of course microscopically, electrons are in motion.
As your text puts it: “induced emf is produced by a changing
magnetic field.”
21.2 Faraday’s Law
To quantify the ideas of section 21.1, we define magnetic flux.
In an earlier chapter we briefly touched on electric flux. This
is the magnetic analog.
Because we can’t “see” magnetic
fields directly, we draw magnetic
field lines to help us visualize the
magnetic field.
Remember that magnetic field
lines start at N poles and end at S
poles.
A strong magnetic field is represented by many magnetic field
lines, close together. A weak magnetic field is represented by
few magnetic field lines, far apart.
Field is strong in this region.
Field is weak in this region.
We could, if we wished, actually “calibrate” by specifying the number of magnetic
field lines passing through some surface that corresponded to a given magnetic
field strength.
Magnetic flux B is proportional to the number of magnetic
field lines passing through a surface.
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/fluxmg.html
Mathematically, magnetic flux B
through a surface of area A is
defined by
B
A
B = B A cos
OSE:
B = BA
where B is the component of field
perpendicular to the surface, A is
the area of the surface, and is
the angle between B and the
normal to the surface.
B
B
A
When B is parallel to the surface,
=90° and B = 0.
When B is perpendicular to the
surface, =0° and B = BA.
B
A
B=0
B=0
=0
A
B
The unit of magnetic flux is the Tm2, called a weber:
1 Wb = 1 T m2 .
In the following discussion, we switch from talking about
surfaces in a magnetic field…
…to talking about loops of wire in a magnetic field.
Now we can quantify the induced emf described qualitatively
in the previous section
Experimentally, if the flux through N loops of wire changes by
an amount B in a time t, the induced emf is
ΔφB
ε = -N
.
Δt
This is called Faraday’s law of
induction. It is one of the
fundamental laws of electricity and
magnetism, and an important
component of the theory that
explains electricity and magnetism.
I wonder why the – sign…
Not an OSE—
not quite yet.
ΔφB
ε = -N
.
Δt
Experimentally…
…an induced emf always gives rise to a current whose
magnetic field opposes the change in flux—Lenz’s law.*
Think of the current resulting from the induced emf as “trying”
to maintain the status quo—to prevent change.
*We’ll practice with this in a bit.
If Lenz’s law were not true—if there were a + sign in faraday’s
law—then a changing magnetic field would produce a current,
which would further increased the magnetic field, further
increasing the current, making the magnetic field still bigger…
Among other things, conservation of energy would be
violated.
Ways to induce an emf:
change B
change the area of the loop in the field
Ways to induce an emf (continued):
change the orientation of the loop in the field
Conceptual example 21-1 Induction Stove
An ac current in a coil in the stove
top produces a changing
magnetic field at the bottom of a
metal pan.
The changing magnetic field gives
rise to a current in the bottom of
the pan.
Because the pan has resistance, the current heats the pan. If
the coil in the stove has low resistance it doesn’t get hot but
the pan does.
An insulator won’t heat up on an induction stove.
Remember the controversy about cancer from power lines a few years
back? Careful studies showed no harmful effect. Nevertheless, some
believe induction stoves are hazardous.
got to here, lect 14 fs2002
Conceptual example 21-2 Practice with Lenz’s Law
In which direction is the current induced in the coil for each
situation shown?
(counterclockwise)
(no current)
(counterclockwise)
(clockwise)
Rotating the coil about the vertical diameter
by pulling the left side toward the reader
and pushing the right side away from the
reader in a magnetic field that points from
right to left in the plane of the page.
(counterclockwise)
Remember
ΔφB
ε = -N
?
Δt
Now that we are experts on the application of Lenz’s law, lets
make our induced emf equation official:
ΔφB
ε = N
.
Δt
This means it is up to you to use Lenz’s law to
figure out the direction of the induced current (or
the direction of whatever the problem wants.
Example 21-3 Pulling a Coil from a Magnetic Field
A square coil of side 5 cm contains 100 loops and is positioned
perpendicular to a uniform 0.6 T magnetic field. It is quickly
and uniformly pulled from the field (moving to B) to a region
where the field drops abruptly to zero. It takes 0.10 s to
remove the coil, whose resistance is 100 .
5 cm
B = 0.6 T
(a) Find the change in flux through the coil.
Initial: Bi = BA .
Final: Bf = 0 .
B = Bf - Bi = 0 - BA = - (0.6 T) (0.05 m)2 = - 1.5x10-3 Wb
.
(b) Find the current and emf induced.
final
initial
The current must flow counterclockwise to induce a downward
magnetic field (which replaces the “removed” magnetic field).
The induced emf is
ΔφB
ε = N
Δt
ε = 100
-3
-1.5×10
Wb
0.1 s
ε = 1.5 V
The induced current is
I =
ε
R
=
1.5 V
100 Ω
= 15 mA .
(c) How much energy is dissipated in the coil?
Current flows “only*” during the time flux changes.
E = Pt = I2Rt = (1.5x10-2 A) (100 ) (0.1 s) = 2.3x10-3 J .
(d) What was the average force required?
The loop had to be “pulled” out of the magnetic field, so the
pulling force did work. It is tempting to try and set up a free
body diagram and use Newton’s laws. Instead, energy
conservation gets the answer with less brainwork.
*If there no resistance in the loop, the current would flow indefinitely.
However, the resistance quickly halts the flow of current once the magnetic
flux stops changing.
The flux change occurs only when the coil is in the process of
leaving the region of magnetic field.
No
No
No
No
flux change.
emf.
current.
work (why?).
Fapplied
D
Flux changes. emf induced. Current flows. Work
done.
No flux change. No emf. No current. (No work.)
The energy calculated in part (c) is the energy dissipated in
the coils while the current is flowing. The amount calculated
in part (c) is also the mechanical energy put into the system
by the force.
Ef – Ei = [ Wother]If
0
See 2 slides back
Ef – Ei = F D
for F and D.
F = Ef / D
F = (2.3x10-3 J) / (0.05 m)
F = 0.046 N