Download 4.1 The Concepts of Force and Mass

Electromagnetic
Induction
21.7 Magnetic Fields Produced by Currents
• In 1820, H.C. Oersted
discovered that a current in a wire
caused a deflection in a magnet.
• This led to the conclusion that
moving charges were magnets,
producing their own magnetic field
and exerting forces on other
magnets.
• It seemed natural for scientists
to investigate the opposite: Can a
magnet generate a potential
difference and thus cause current
flow, in much the same way as a
battery?
“Induced” Current
• A current creates a
magnetic field.
• Is the opposite true?
• Can a magnetic field
create, or induce a
current?
• In 1831, Michael
Faraday made an
exciting discovery
Faraday’s Discovery
• To test this hypothesis, Faraday used 2 separate
circuits that were not connected and wrapped each
around an iron ring that did not conduct electricity.
• He thought by closing the switch on the left, the
magnetic field of the left wire would magnetize the
iron ring, which in turn might induce a current in
the wire on the right.
• But no luck, as the meter shows.
Faraday’s Discovery
• Disappointed, he shut
down for lunch.
• But when he opened the
switch to cut off the
current in the left circuit,
the meter suddenly
moved, showing a
momentary current in the
wire on the right.
• It quickly went back to
zero.
Faraday’s Discovery
• Baffled, he closed
the switch again.
• And noticed that the
meter jumped again
momentarily, and this
time the meter needle
went the other way.
• I bet he actually did it
a bunch of times
before he noticed that
it went the other way..
Faraday’s Law
• Faraday found that he could induce a current
in a closed coil of wire with an external
magnetic field, but only if the magnetic field
through the coil is changing.
• This is an informal statement of Faraday’s
Law.
• A moving magnetic field causes charge to
flow, just as moving charge causes a magnet
to deflect.
22.1 Induced Emf and Induced Current
There are a number of ways a magnetic field can be used to
generate an electric current.
It is the changing magnetic field that produces the current.
A square loop of copper wire is pulled through a
region of constant magnetic field. In which case,
if any, does current flow?
A. 2,3,4 B. None C. 2,4
D. All
1
2
3
4
22.1 Induced Emf and Induced Current
We know that a current is induced in the presence
of a changing magnetic field.
How do we calculate the magnitude and direction
of the current?
To do so, we must discuss a quantity called the
magnetic flux, Φ.
22.3 Magnetic Flux
GRAPHICAL INTERPRETATION OF MAGNETIC FLUX
We can think as the
magnetic flux as
proportional to the number
of magnetic field lines that
pass through a surface.
We can change the
magnetic flux by:
• changing the magnetic
field strength(B) as shown
• changing the size of the
loop
• changing the angle
between the normal to the
loop and the direction of B
Magnetic Flux due to an external magnetic field
Φm = AB cos θ
A = cross-sectional area of the loop (m2 )
B = strength of magnetic field (Tesla)
θ = angle between B, and normal to A
Units: 1 weber = 1Wb = 1Tm2
Rank the magnitude of magnetic flux that passes
through the coil, shown below (edge view) in three
different orientations relative to an external
magnetic field. Rank from greatest flux to least.
a. 1,2,3
b. 3,2,1
c. (1,3), 2
d.(3,1), 2
Magnetic Flux
A uniform magnetic field
has a magnitude of
0.078 T and is
uniform over a
circular surface of
radius 0.10 m. The
field is oriented at an
angle of 25˚ with
respect to the normal
of the surface. What
is the magnetic flux
through the surface?
Magnetic Flux
A uniform magnetic field
has a magnitude of
0.078 T and is
uniform over a
circular surface of
radius 0.10 m. The
field is oriented at an
angle of 25˚ with
respect to the normal
of the surface. What
is the magnetic flux
through the surface?
Answer: 2.2 x 10-3 Wb
Change in Magnetic flux
A long, narrow rectangular
loop of wire is moving
toward the bottom of the
page with a speed of 0.019
m/s (see the drawing). The
loop is leaving a region in
which a 2.1 T magnetic field
exists; the magnetic field
outside this region is zero.
During a time of 1.0 s, what
is the magnitude of the
change in the magnetic flux?
Change in Magnetic flux
A long, narrow rectangular
loop of wire is moving
toward the bottom of the
page with a speed of 0.019
m/s (see the drawing). The
loop is leaving a region in
which a 2.1 T magnetic field
exists; the magnetic field
outside this region is zero.
During a time of 1.0 s, what
is the magnitude of the
change in the magnetic flux?
Ans: .00319 Tm2 or Wb
22.4 Faraday’s Law of Electromagnetic Induction
• Faraday found that he could induce a current in a closed
coil of wire with an external magnetic field, but only if the
magnetic field through the coil is changing. This is an
informal statement of Faraday’s Law.
• The formal statement relates the changing magnetic flux
to an induced emf (ε), which is the potential difference that
causes a current to flow in a closed conductor. The
magnitude of ε, the emf, induced in a coil of N loops is:
   o 

  N
  N 
t
 t  to 
SI Unit of Induced Emf: volt (V)
22.4 Faraday’s Law of Electromagnetic Induction
Example 5 The Emf Induced by a Changing Magnetic Field
A coil of wire consists of 20 turns each of which has an area of 0.0015 m2.
A magnetic field is perpendicular to the surface. Initially, the magnitude of
the magnetic field is 0.050 T and 0.10s later, it has increased to 0.060 T.
Find the average emf induced in the coil during this time.
BA cos   Bo A cos 

EN
N
t
t
0.060 T  0.050 T
 B  Bo 
2
 NA cos  
  20 0.0015 m cos0
0.10 s
 t 
 3.0 10 3 V


(Worksheet) Flux Ranking Task
(Worksheet)Changing Flux
An MRI
Magnetic resonance imaging (MRI) is a medical technique
for producing pictures of the interior of the body. The
patient is placed within a strong magnetic field. One
safety concern is what would happen to the positively and
negatively charged particles in the body fluids if an
equipment failure caused the magnetic field to be shut off
suddenly. An induced emf could cause these particles to
flow, producing an electric current within the body.
Suppose the largest surface of the body through which
flux passes has an area of 0.026 m2 and a normal that is
parallel to a magnetic field of 3.5 T. Determine the
smallest time period during which the field can be allowed
to vanish if the magnitude of the average induced emf is
to be kept less than 0.010 V.
An MRI
Magnetic resonance imaging (MRI) is a medical technique
for producing pictures of the interior of the body. The
patient is placed within a strong magnetic field. One safety
concern is what would happen to the positively and
negatively charged particles in the body fluids if an
equipment failure caused the magnetic field to be shut off
suddenly. An induced emf could cause these particles to
flow, producing an electric current within the body.
Suppose the largest surface of the body through which
flux passes has an area of 0.026 m2 and a normal that is
parallel to a magnetic field of 3.5 T. Determine the
smallest time period during which the field can be allowed
to vanish if the magnitude of the average induced emf is to
be kept less than 0.010 V.
Ans: 9.1 s
A current-carrying wire is pulled away from a copper
wire loop as shown. As a result, an emf (and
therefore a current) is induced in the loop. To
maximize the emf, we should:
A. pull the wire away from the loop more slowly
B. pull the wire away from the loop more quickly
C. push the wire towards the loop at the same speed.
Lenz’s Law
• There is an induced
current in a closed
conducting loop only if
the magnetic flux is
changing (either B, A
or θ). The direction of
the induced current is
such that the induced
magnetic field
opposes the change in
flux.
Using Lenz Law
1. Determine the direction of the external magnetic
field.
2. Determine how the flux is changing. Is it increasing,
decreasing, or staying the same?
3. Determine the direction of an induced magnetic field
that will oppose the change in the flux.
– Increasing: induced magnetic field points opposite
the external magnetic field.
– Decreasing: induced magnetic field points in the
same direction as the external magnetic field.
– Constant: no induced magnetic field.
4. Determine the direction of the induced current. Use
the right-hand rule.
Lenz’s Law
An induced current in a
coil or loop can be
created 2 ways:
– Change the size or
orientation of the coil
in a stationary
magnetic field.
– Change the strength
of the magnetic field
through a stationary
circuit.
Both of these create a
changing magnetic
flux.
The current exists
because the
changing magnetic
flux has induced an
emf. In a closed
circuit with a
resistance, R:
I = ε/R
The current is a
consequence of the
induced emf.
The emf is a
consequence of
changing flux (Φm )
http://phet.colorado.edu/en/simulation/faraday
Lenz’s Law
An external magnetic
field, B is directed
into the page. A
sliding rail
completes the
circuit. The rail is
pushed to the right,
increasing the area
of the circuit.
Lenz’s Law
In which direction is
the induced
magnetic field?
a. into the page
b. out of the page
c. zero, since field is
stationary
d. in the direction of the
moving rail
Lenz’s Law
A current-carrying wire is pulled away from a copper
wire loop as shown. As a result, an emf (and
therefore a current) is induced in the loop. in what
direction is the current?
A. clockwise
B. counterclockwise
C. No current
Is the induced current cw, ccw or zero?
a. The external magnetic
field is increasing
b. The external magnetic
field is decreasing
c. The right side of the loop
turns into the page
d. The left side of the loop
turns into the page
Positive (+) current comes out the top of the loop and
enters the bottom.
Negative (-) current comes out the bottom of the loop and
enters the top.
For A and B, and C is the current +, -, or zero?
A.
B.
C.
D.
The magnet is pushed into the loop.
The magnet is pulled back to the left.
The loop turns so the normal is in the plane of the page.
If the magnet is pulled out more loop more rapidly than in
A, does the current increase, decrease or stay the same?