# Electromagnetic Induction by dfhdhdhdhjr

VIEWS: 4 PAGES: 21

• pg 1
```									    Electromagnetic Induction
Objective:
TSW understand and apply the concept of
magnetic flux in order to explain how
induced emfs are created and calculate
their value and polarity.
You will be responsible for the content contained in
chapter 20, sections 1&2 of the textbook. Take the

Chapter 20 Homework Problems:
4, 9, 15, 17, 19, 22, 23
Electromagnetic induction is the process
by which an emf (voltage) is produced in a
wire by a changing magnetic flux.

• Magnetic flux is the product of the
magnetic field and the area through which
the magnetic field passes.
• Electromagnetic induction is the principle
behind the electric generator.
• The direction of the induced current due to
the induced emf is governed by Lenz’s
Law.
Here is a visual model of what we
did in chapter 19:

Loop of wire
Output
Input         and an
Force
Current       External
(wire moves)
magnetic field

Electric Motor
Here is a visual model of what we
will do in chapter 20:

Loop of wire
Input
and an        Output
Force
External       Current
(move wire)
magnetic field

Generator
The next two slides contain
vocabulary and equations, you
should commit them to
memory
Important Terms
alternating current - electric current that rapidly reverses its direction
electric generator - a device that uses electromagnetic induction to
convert mechanical energy into electrical energy
electromagnetic induction - inducing a voltage in a conductor by
changing the magnetic field around the conductor
induced current - the current produced by electromagnetic induction
induced emf - the voltage produced by electromagnetic induction
Faraday’s law of induction - law which states that a voltage can be
induced in a conductor by changing the magnetic field around the
conductor
Lenz’s law - the induced emf or current in a wire produces a magnetic
flux which opposes the change in flux that produced it by
electromagnetic induction
magnetic flux - the product of the magnetic field and the area through
which the magnetic field lines pass.
motional emf - emf or voltage induced in a wire due to relative motion
between the wire and a magnetic field
Equations, Symbols, and Units
where
  BLv       ε = emf (voltage) induced by
electromagnetic induction (V)


v = relative speed between a conductor

I
and a magnetic field (m/s)
B = magnetic field (T)
R         L = length of a conductor in a magnetic

  BAcos
field (m)
I = current (A)
R = resistance (Ω)
     Φ = magnetic flux (Tm2 = Weber=Wb)
  N        A = area through which the flux is
t          passing (m2)
= angle between the direction of the
P  IV             magnetic field and the area through
which it passes
Magnetic Flux
Consider a rectangular loop of wire of height L and width x
which sits in a region of magnetic field of strength B. The
magnetic field is directed into the page, as shown below:
w

L

The magnetic flux is given by the following equation:

  BAcos                  Φ = The magnetic flux (Tm2 = Wb)
B = The magnetic field (T)
A = area of loop (m2)
Φ = angle between the field and the area
Faraday’s law states that an induced emf is
produced by changing the flux, but how
could the flux be changed?
• Turn the field off or on.
• Move the loop of wire out of the field
• Rotate the loop to change the angle
between the field and the area of the loop.
Here is Faraday’s Law in equation
form:

Where
                        Є = The induced emf (voltage) (V)
N                           ΔΦ = The change in flux (Wb)
t                        Δt = The change in time (s)
N = number of loops.

*Note that an emf is only produced if the flux changes. The quicker the
flux changes the larger the induced emf.
The induced emf in the wire will produce a current in the wire. The
magnitude of the induced current is found using Ohm’s Law:

V  IR
  IR

I
R
The direction of the induced current is found using Lenz’s Law (conservation of
energy).

Lenz’s Law – The induced current in a wire produces a
magnetic field such the flux of the produced magnetic
field opposes the original change in flux. In simple
terms the wire resists the change in flux and wants to
go back to the way things were.
It is helpful to use RHR#2 when using Lenz’s Law.
Example 1: A circular loop of wire with a resistance of 0.5Ω and
radius 30cm is placed in an external magnetic field of 0.2T. The
magnetic field is turned off in .02 seconds.
a) Calculate the original flux of the loop.
b) Calculate the induced emf.
c) Calculate the current induced in the wire.
d) What direction does the induced current have?
e) What other way could the same emf be induced without turning the
field off?
•        •        •     •
•        •        •     •
•        •        •     •
•        •        •     •
•        •        •     •
Let’s do some examples
predicting the induced current
direction using Lenz’s Law
•       •        •         •   •      •         •         •
•       •        •         •   •      •         •         •
•       •        •         •   •      •         •         •
•       •        •         •   •      •         •         •
•        •        •
Bout decreasing flux   •   •      •         •
Bout increasing flux
•
CCW                             CW

X       X         X        X   X     X         X          X
X       X         X        X   X     X         X          X
X       X         X        X   X     X         X          X
X       X         X        X   X     X         X          X
X       X         X        X   X     X         X          X
Bin decreasing flux           Bin increasing flux
CW                           CCW
If you are really struggling applying Lenz’s
Law, then memorize the following table:

decreasing   Increasing

B out        CCW          CW

B in        CW          CCW
Example 2: A circuit with a total resistance of 5Ω is made using a set
of metal wires and a copper bar. The magnetic field is directed into
the page as shown in the diagram. The bar starts on the left and is
pulled to the right at a constant velocity.
a) Calculate the induced emf in the circuit.
b) Calculate the current induced in the wire.
c) What direction does the induced current have?
d) What is the magnitude and direction of the magnetic force that
opposes the motion of the bar?
X       X        X       X          X       X   X
X       X        X       X          X       X   X
X       X        X       X          X   v   X   X
L
X       X        X       X          X       X   X
X       X        X       X          X       X   X
X       X        X       X          X       X   X
The last example led to the equation for the motional emf.
The motional emf is the voltage induced in a wire as it
moves in an external magnetic field. The induced emf will
produce a current in the wire, which will in turn result in a
force that opposes the motion of the wire. You don’t get
something for nothing.

Motional emf                 Where
Є = The induced emf (V)
B = The external magnetic field (T)

  BLv                 L = The length of the wire (m)
v = The velocity of the wire (m/s)
Example 3: A conducting rod of length 0.30 m and resistance 10.0 Ω
moves with a speed of 2.0 m/s through a magnetic field of 0.20 T which is
directed out of the page.
v

L

B (out of the
page)

a) Find the emf induced in the rod.
b) Find the current in the rod and the direction it flows.
c) Find the power dissipated in the rod.
d) Find the magnetic force opposing the motion of the rod.
Example 4: A square loop of sides a = 0.4 m, mass m =
1.5 kg, and resistance 5.0 Ω falls from rest from a
height h = 1.0 m toward a uniform magnetic field B
a
which is directed into the page as shown.
(a) Determine the speed of the loop just before it enters
a
the magnetic field.

As the loop enters the magnetic field, an emf ε and a
current I is induced in the loop.
(b) Is the direction of the induced current in the loop
h
clockwise or counterclockwise? Briefly explain how

When the loop enters the magnetic field, it falls through
with a constant velocity.                                              B

(c) Calculate the magnetic force necessary to keep the
loop falling at a constant velocity.
(d) What is the magnitude of the magnetic field B
necessary to keep the loop falling at a
constant velocity?
(e) Calculate the induced emf in the loop as it enters and
exits the magnetic field.

```
To top