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CONCLUSION – CHAPTER 20 &
CHAPTER 21 – ELECTROMAGNETIC
INDUCTION
Chapter 21
Quick Review IB
0 I
B
2r
r
Tm
0  4 10
(exact)
A
7
2
Magnetism
Force Between Two Current
Carrying Conductors
First wire produces a magnetic field at the
second wire position.
The second wire therefore feels a force = Bil
3
Magnetism
Solenoid
B   0 nI
Total number
N of Turns
n 
L
Length
B=~0 outside
4
Magnetism
The Toroid–
 0 NI
B
2r
B=0 outside
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Magnetism
A rectangular loop has sides of length 0.06 m and 0.08
m. The wire carries a current of 10 A in the direction
shown. The loop is in a uniform magnetic field of
magnitude 0.2 T and directed in the positive x direction.
What is the magnitude of the torque on the loop?
  NIAB sin(  )
8 × 10–3 N × m
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Magnetism
A solenoid of length 0.250 m and
radius 0.0250 m is comprised of 440
turns of wire. Determine the
magnitude of the magnetic field at
the center of the solenoid when it
carries a current of 12.0 A.
2.21 × 10–3 T
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Magnetism
The drawing shows two long, thin wires that
carry currents in the positive z direction. Both
wires are parallel to the z axis. The 50-A wire is
in the x-z plane and is 5 m from the z axis. The
40-A wire is in the y-z plane and is 4 m from the
z axis. What is the magnitude of the magnetic
field at the origin?
B
0 I
2r
0  4 107
Tm
(exact)
A
3 × 10–6 T
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Magnetism
I
I
9
Moving On to the next
chapter……………….
Magnetism
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INTRODUCTION TO INDUCTION
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Important Definition – Magnetic Flux
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Magnetic Field
AREA
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The Essence of this Topic
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




Consider a conductor that is shaped in a loop but is
continuous.
The conductor has a magnetic field through the loop
that is not necessarily uniform.
There is a MAGNETIC FLUX through this loop.
If the FLUX CHANGES, an “emf” will be induced
around the loop.
This emf can cause a current to flow around the
loop.
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How Can You Change the Magnetic
Flux Going Through The Loop? Huh?
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


Divide the area of the
loop into a very large
number of small areas
DA.
Find the Magnetic Field
through each area as
well as the angle that it
makes with the normal to
the area.
Compute the total flux
through the loop.
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The Magnetic Flux Going Through The
Loop:
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   Bi cos(i )DAi
i
Add up all of these pieces
that are INSIDE the loop.
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Changing 
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
Change any or all of the
 Bi
 DAi
 i
 Change
the SHAPE of the loop
 Change the ANGLE that the loop makes
with the magnetic field (subset of above)

And the Flux will change!
   Bi cos(i )DAi
i
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WAIT A SECOND …….
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



You said that there is a conducting loop.
You said that there is therefore a VOLTAGE or emf
around the loop if the flux through the loop
changes.
But the beginning and end point of the loop are the
same so how can there be a voltage difference
around the loop?
‘tis a puzzlement!
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REMEMBER when I said E Fields start
and end on CHARGES???
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DID I LIE??
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The truth
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

Electric fields that are created by static charges
must start on a (+) charge and end on a (–) charge
as I said previously.
Electric Fields created by changing magnetic fields
can actually be shaped in loops.
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Why do you STILL think I am a liar?
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Because you said that an
emf is a voltage so if I
put a voltmeter from one
point on the loop around
to the same point, I will
get ZERO volts, won’t I
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The POTENTIAL between two points
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

Is the WORK that an external agent has to do to
move a unit charge from one point to another.
But we also have (neglecting the sign):
DV   EDs
Ds
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So, consider the following:
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emf   EDs  E  Ds
x
x
x
x
x
x
x
x
x
x
x
x
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x
x
x
x
x
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x
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x
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x
x
x
x
x
x
x
x
x
x
x
x
x
x
emf  2RE  zero
E
Conductor
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THEREFORE WHAT WILL A VOLTMETER
READ FROM A to A?
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x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
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x
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x
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x
x
x
x
x
x
x
x
x
x
x
x
x
E
A
B
C
The emf
Zero
Can’t tell

A
Conductor
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emf  
MINUS????
DThrough
the loop
Dt
Michael Faraday
(1791-1867)
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Q: Which way does E point?
A: The way that you don’t want it to
point! (Lenz’s Law).
Lenz’s Law Explains the (-) sign!
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OK. LET’S DO THE PHYSICS NOW
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Is there an induced current???
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Induction Effects
Faraday’s Experiments
?
?
Insert Magnet into Coil
Remove Coil from Field Region
Summary
Does the Flux Change?
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In the Previous Example, if there are N
coils rather than a single coil,
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A
B
C
The current is increased by a factor of N
The current is decreased by a factor of N
The current stays the same.
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Push a magnet into a coil of two wires
and a current is produced via an emf.
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In this case, 2 coils, each has
the SAME emf.
Ohm’s Law still works, so
D
emf  N
Dt
emf
i
Rcoil
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If we go from 2 to 4 coils, the current
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A
B
C
D
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Stays the same
Doubles
Is halved
Is four times larger
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A rectangular circuit containing a resistor is perpendicular to
a uniform magnetic field that starts out at 2.65 T and steadily
decreases at 0.25 T/s. While this field is changing, what does
the ammeter read?
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••The conducting rod ab shown makes frictionless
contact with metal rails ca and db. The apparatus is in
a uniform magnetic field of 0.800 T, perpendicular to
the plane of the figure. (a) Find the magnitude of the
emf induced in the rod when it is moving toward the
right with a speed 7.50 m/s.
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emf  AB sin t
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Almost DC
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THE STRANGE WORLD OF DR. LENTZ
LENZ’S LAW
Induced Magnetic Fields always FIGHT to
stop what you are trying to do!
i.e... Murphy’s Law for Magnets
Example of Nasty Lenz
The induced magnetic field opposes the
field that does the inducing!
Don’t Hurt Yourself!
The current i induced in the loop has the direction
such that the current’s magnetic field Bi opposes the
change in the magnetic field B inducing the current.
Let’s do the
Lentz Warp
again !
Again: Lenz’s Law
An induced current has a direction
such that the magnetic field due to
the current opposes the change in
the magnetic flux that induces the
current. (The result of the
negative sign that we always leave
out!) …
OR
The toast will always fall buttered side down!
What Happens Here?



Begin to move handle as
shown. Assume a
resistance R in the loop.
Flux through the loop
decreases.
Current is induced which
opposed this decrease –
current tries to reestablish the B field.
What about a SOLID loop??
Energy is LOST
BRAKING SYSTEM
METAL
Pull
A cardboard tube is wrapped with two windings of insulated
wire, as shown. Is the induced current in the resistor R directed
from left to right or from right to left in the following
circumstances?
The current in winding A is directed
(a) from a to b and is increasing,
(b) from b to a and is decreasing,
(c) from b to a and is increasing, and
(d) from b to a and is constant.
left
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Induction
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Mutual inductance –
Circulation of currents in one
coil can generate a field in the
coil that will extend to a second,
close by device.

Flux Changes
Suppose i1 CHANGES
Current (emf) is
induced in 2nd
coil.
The two coils
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Remember – the magnetic
field outside of the solenoid
is pretty much zero.
Two fluxes (fluxi?) are the same!
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Self-inductance –
Any circuit which carries a varying current self-induced
from it’s own magnetic field is said to have INDUCTANCE
(L).

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An inductor resists CHANGES in the
current going through it.
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An inductor resists CHANGES in the
current going through it.
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An inductor resists CHANGES in the
current going through it.
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Inductance Defined
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N B
L
i
If the FLUX changes a but during a short time
Dt, then the current will change by a small
amount Di.
Li  N B
Faraday says
this is the emf!
D B
Di
N
L
Dt
Dt
This is actually a
calculus equation
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So …
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Di
E= emf  L
Dt
There should be
a (-) sign but we
use Lenz’s Law
instead!
The UNIT of “Inductance – L” of a coil is the henry.
SYMBOL:
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Consider “AC” voltage
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Minimum Change/Dt
V1
Maximum Change/Dt
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The transformer
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D
emf1  V1  N1
Dt
FLUX is the same through
both coils (windings).
D
emf 2  V2  N 2
Dt
V1 V2

N1 N 2
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Input/Output Impedance (Resistance)
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V2 N 2

V1 N1
Powerin  Powerout (Lossless)
I1V1  I 2V2
So
V1
R

I1 ( N 2 / N1 ) 2
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 looks like an input 


resistance !


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Read in the textbook section 21.10:
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2
Energy
B
u

Unit  Volume 20
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Energy associated with an induced
current.
As energy is introduced at induces a field, energy is stored in
an electronic device.
 Refer to worked example 21.12 in your text.

The R-L circuit – Figure 21.29
When an
inductor is part of
a wired circuit, voltages, currents
and capacitor
charges are a
function of time,
not constants.
 Refer to worked
example 21.13 in
your text.

The L-C circuit – Figure 21.34
When an inductor is part of a wired circuit with a capacitor, the
capacitor charges over time.
 Commonly used in radio as a tuner for the induced current from
an antenna.
