magnetic induction
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Physics 72 Bareza AY 15-16 1st sem 2
If the magnetic flux through a circuit changes,
an emf and a current are induced in the circuit.
Electromagnetic Induction
A time-varying magnetic field can act as a source of electric field.
A time-varying electric field can act as a source of magnetic field.
Maxwell’s equations.
Chapter 29
Magnetic Induction
29-1 Induction Experiment29-2 Faraday’s Law29-3 Lenz’s Law29-4 Motional Electromotive Force29-5 Induced Electric Fields
Physics 72 Bareza AY 15-16 1st sem 3
Objective
• Identify the factors that affect the magnitude of the induced EMF and the magnitude and direction of the induced
current
Physics 72 Bareza AY 15-16 1st sem 4
Physics 72 Bareza AY 15-16 1st sem 5
We connect a coil of wire to a galvanometer, then place the
coil between the poles of an electromagnet whose magnetic
field we can vary. Here’s what we observe:
When there is no current in the
electromagnet, so that B = 0, the
galvanometer shows no current.
When the electromagnet is turned on,
there is a momentary current through the
meter as B increases.
When B levels off at a steady value, the
current drops to zero, no matter how
large B is.
Physics 72 Bareza AY 15-16 1st sem 6
With the coil in a horizontal plane, we squeeze
it so as to decrease the cross-sectional area
of the coil. The meter detects current only
during the deformation, not before or after.
When we increase the area to return the coil to
its original shape, there is current in the
opposite direction, but only while the area of the
coil is changing.
If we rotate the coil a few degrees about a
horizontal, the meter detects current during the
rotation, in the same direction as when we
decreased the area. When we rotate the coil
back, there is a current in the opposite direction
during this rotation.
Physics 72 Bareza AY 15-16 1st sem 7
If we jerk the coil out of the magnetic field, there
is a current during the motion, in the same
direction as when we decreased the area.
If we decrease the number of turns in the coil by
unwinding one or more turns, there is a current
during the unwinding, in the same direction as
when we decreased the area. If we wind more
turns onto the coil, there is a current in the
opposite direction during the winding.
Physics 72 Bareza AY 15-16 1st sem 8
When the magnet is turned off, there is a
momentary current in the direction opposite
to the current when it was turned on.
The faster we carry out any of these
changes, the greater the current.
Physics 72 Bareza AY 15-16 1st sem 9
If all these experiments are repeated with a
coil that has the same shape but different
material and different resistance, the
current in each case is inversely
proportional to the total circuit
resistance. This shows that the induced
emfs that are causing the current do not
depend on the material of the coil but
only on its shape and the magnetic field.
Physics 72 Bareza AY 15-16 1st sem 10
The common element in all
these experiments is
changing magnetic flux
through the coil
connected to the
galvanometer.
Physics 72 Bareza AY 15-16 1st sem 11
Different ways for induction:(1) Changing magnetic field strength
(2) Changing Area
(3) Changing relative orientation between
magnetic field and area vector
*with the condition that magnetic field and
area vector is not completely perpendicular
for (1) and (2)
Chapter 29
Magnetic Induction
29-1 Induction Experiment29-2 Faraday’s Law29-3 Lenz’s Law29-4 Motional Electromotive Force29-5 Induced Electric Fields
Physics 72 Bareza AY 15-16 1st sem 12
Objective
• Calculate the induced EMF in a closed loop due to a time-varying magnetic flux using Faraday’s Law
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Physics 72 Bareza AY 15-16 1st sem 13
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Physics 72 Bareza AY 15-16 1st sem 14
Faraday's law of induction
The induced emf in a closed loop equals the
negative of the time rate of change of magnetic
flux through the loop.
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Physics 72 Bareza AY 15-16 1st sem 15
Magnetic Flux
Magnetic Flux thru an open surface
If is uniform, then
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Physics 72 Bareza AY 15-16 1st sem 16
Direction of the induced emf
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Physics 72 Bareza AY 15-16 1st sem 17
Direction of the induced emf
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Physics 72 Bareza AY 15-16 1st sem 18
If we have a coil with N identical turns, the total emf
in a coil with N turns is
Magnetic flux through a single coil
Where:
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Physics 72 Bareza AY 15-16 1st sem 19
The figure shows a wire coil being
squeezed in a uniform magnetic field.
While the coil is being squeezed, is
the induced emf in the coil
A. clockwise,
B. counterclockwise, or
C. zero?
Once the coil has reached its final
squeezed shape, is the induced emf
in the coil
A. clockwise,
B. counterclockwise, or
C. zero?
Example:
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Physics 72 Bareza AY 15-16 1st sem 20
Example:
Answers:(a) emf = 0.0900*0.190 V(b) I = 0.0900*0.190/0.600 A
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Physics 72 Bareza AY 15-16 1st sem 21
Example:
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Physics 72 Bareza AY 15-16 1st sem 22
Seatwork:A conducting loop is placed perpendicular to a constant
uniform magnetic field as shown. If the area of the loop
increases at a rate α, find the following.
a) Induced emf ε
b) Direction of induced current
(Answer: ε = -Bα, |ε| = Bα)
(Answer: CW)
Chapter 29
Magnetic Induction
29-1 Induction Experiment29-2 Faraday’s Law29-3 Lenz’s Law29-4 Motional Electromotive Force29-5 Induced Electric Fields
Physics 72 Bareza AY 15-16 1st sem 23
Objective
• Describe the direction of the induced electric field, magnetic field and current on a conducting/non-conducting
loop using Lenz’s Law
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Physics 72 Bareza AY 15-16 1st sem 24
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Physics 72 Bareza AY 15-16 1st sem 25
Lenz’s Law
The direction of any magnetic induction effect is
such as to oppose the cause of the effect.
The induced emf and induced current are in
such a direction as to oppose the change
that produces them.
It gives only the direction of induced emf and current.
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Physics 72 Bareza AY 15-16 1st sem 26
Lenz’s Law
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Physics 72 Bareza AY 15-16 1st sem 27
Recall:
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Physics 72 Bareza AY 15-16 1st sem 28
Recall:
Example:
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Physics 72 Bareza AY 15-16 1st sem 29
Explanation: Through RHR, B due to I inside coil is out of the page. The B strength decreases through time since B is proportional to I due to wire. B induced on coil is out of the page due to decreasing B strength via Lenz’s law.Answer: current is CCW using RHR.
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Physics 72 Bareza AY 15-16 1st sem 30
Example:Answers:(a) CCW(b) CW(c) none
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Physics 72 Bareza AY 15-16 1st sem 31
IP
Seatwork:A very long wire is part of a circuit with
a switch. Beside it is a conducting loop.
The switch, initially open, was closed
causing a current to flow. During the
switching, what is
a) the direction of the induced magnetic
field inside the coil?
b) the direction of the induced current
through point P?
Out of the page
Downward
Chapter 29
Magnetic Induction
29-1 Induction Experiment29-2 Faraday’s Law29-3 Lenz’s Law29-4 Motional Electromotive Force29-5 Induced Electric Fields
Physics 72 Bareza AY 15-16 1st sem 32
Objective
• Given the velocity and the orientation of a conductor in a uniform magnetic field, determine the induced EMF, electric
field, magnetic field and current
Physics 72 Bareza AY 15-16 1st sem 33
Physics 72 Bareza AY 15-16 1st sem 34
We can gain additional insight into the origin of the
induced emf by considering the magnetic forces on
mobile charges in the conductor.
If a conductor moves in a magnetic field, a motional emf is induced.
Physics 72 Bareza AY 15-16 1st sem 35
Physics 72 Bareza AY 15-16 1st sem 36
The moving rod has become a
source of electromotive force.
motional electromotive force
(length and velocity perpendicular to
uniform magnetic field)
Physics 72 Bareza AY 15-16 1st sem 37
motional electromotive force
If the total circuit resistance of the U-shaped
conductor and the sliding rod is R,
the induced current I in the circuit is given
Physics 72 Bareza AY 15-16 1st sem 38
In general,
More useful in solving problems involving moving conductors!
Applicable only for moving conductors in constant magnetic field
For any conductor with any shape in a uniform or non-uniform magnetic field
For a closed conducting loop
This is always true.
These are the same!
Physics 72 Bareza AY 15-16 1st sem 39
Example:
It requires large velocity to achieve 1.5 V which is still a small voltage so not really.
Physics 72 Bareza AY 15-16 1st sem 40
Example: Answer:(a) emf = 1.5*0.75*5.0(b) All CCW(c) I = 1.5*0.75*5.0/25.0
Physics 72 Bareza AY 15-16 1st sem 41
Seatwork:
Answers:(a) b(b) b(c) None(d) Along direction of -53 deg
ANNOUNCEMENT
• Arrive exactly at 7AM on ThursdayWarning: Recit is relatively longer than your previous ones. This will test your time-budgeting skill. [Coverage: from 29-1 to 29-4]
• Be present on Thursday since take home recit will also be distributed. [Coverage: 29-5 and previous lessons]
Chapter 29
Magnetic Induction
29-1 Induction Experiment29-2 Faraday’s Law29-3 Lenz’s Law29-4 Motional Electromotive Force29-5 Induced Electric Fields
Physics 72 Bareza AY 15-16 1st sem 43
Objective
• Compare and contrast, electrostatic field and non-electrostatic/induced electric field
Physics 72 Bareza AY 15-16 1st sem 44
Physics 72 Bareza AY 15-16 1st sem 45
Physics 72 Bareza AY 15-16 1st sem 46
Question:What force makes the charges move around the loop?
There has to be an induced electric field in the
conductor caused by the changing magnetic flux
(magnetic field).
Recall:
Physics 72 Bareza AY 15-16 1st sem 47
Work done by the induced electric field per unit charge
Induced electric field is not conservative.
Also,
Valid only when integration path is stationary.
Physics 72 Bareza AY 15-16 1st sem 48
Physics 72 Bareza AY 15-16 1st sem 49
Induced Electric Field
Physics 72 Bareza AY 15-16 1st sem 50
A circular conducting loop is immersed in a spatially uniform
magnetic field that is decreasing at a constant rate. Which
of the following best describes the electric field induced in
the loop?
A. Constant and non-conservative
B. Decreasing and non-conservative
C. Increasing and non-conservative
D. Constant and conservative
E. Decreasing and conservative
Example:
In which time interval is the value of the induced
electric field largest for a solenoid with n turns
per meter and radius R at a distance r (r < R) from
the axis of the solenoid?
Seatwork:
Physics 72 Bareza AY 15-16 1st sem 51
ANNOUNCEMENT
• Arrive exactly at 7AM tomorrowWarning: Recit is relatively longer than your previous ones. This will test your time-budgeting skill. [Coverage: from 29-1 to 29-4]
• Be present tomorrow since take home recit will also be distributed. [Coverage: 29-5 and previous lessons]
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