Download Magnetic field

2012.03.26.
What is magnetism?
Magnetism
2012_03_19
Properties of a magnet
For each north pole , there is a south pole
as well!
Word comes from an ancient Greek city called Magnesia, where
many natural magnets were found.
These natural magnets are called now iodestones (iode=
attract), containing magnetite, which is a matural magnetic
material Fe3O4.
Chinese: compass: two places of maximum attraction
Chinese knew, that an iron rod which had been brought near one
these magnets would get and hold this property, and attached
to a string would align in north-south direction.
The use of magnets for navigation can be traced back to the
11th century.
The opposite poles
are attracted to each
other,
N
S
N
S
S
N
Monopoles do not exist!
the same poles repel
each other.
N
S
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2012.03.26.
Magnetic Field
Magnetic field lines.
Magnetic field can be shown with the help of magnetic field
lines.
If we put a compass/needle in a magnetic field, than the needle
will point along the field line.
Michael Faraday realized that a
magnet has a magnetic field
distributed
throughout
the
surrounding space.
One confusion that arises from this definition
is that if Earth itself is considered as a magnet,
the south pole of that magnet would be the
one nearer the north magnetic pole, and viceversa. (Opposite poles attract and the north
pole of the compass magnet is attracted to the
north magnetic pole.) The north magnetic pole
is so named not because of the polarity of the
field there but because of its geographical
location.
Magnetic field can be
characterized with two physical
quantities:
Magnetic field strength vector
Field lines converge
where the magnetic
field is strong and
spread out where it
is weak.
For example bar
magnet the lines
spread out from the
north pole
and
converge
and
closes in the south
pole.
The magnetic field
is the strongest
where the lines are
closer together.
Diverse materials
H
Ferromagnetic materials are the ones normally thought of as 'magnetic';
they are attracted to a magnet strongly enough that the attraction can be
felt. Expl: refrigerator magnet.
Ferrimagnetic materials, which include ferrites and the oldest magnetic
materials magnetite and lodestone, are similar to but weaker than
ferromagnetics.
and magnetic induction
Both are vector quantities
which means they have
direction and magnitude.
0  4 10 Vs / Am
7
B
B    H  0   r  H
Paramagnetic substances such as platinum, aluminum, and oxygen are
weakly attracted to a magnet. This effect is hundreds of thousands of times
weaker than ferromagnetic materials attraction, so it can only be detected
by using sensitive instruments, or using extremely strong magnets..
Diamagnetic means repelled by both poles. Compared to paramagnetic
and ferromagnetic substances, diamagnetic substances such as carbon,
copper, water, and plastic are even more weakly repelled by a magnet. The
permeability of diamagnetic materials is less than the permeability of a
vacuum.
Magnetic permeability of vacuum
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2012.03.26.
Untill now we talked about natural
magnets and their magnetic fields.
But not only magnets can have
magnetic fields but
In 1820 Oersted made an experiment:
Without current: needle/compass showed to the Earth’s
magnetic poles.
With current: Needle/compass showed in the current
generated magnetic field.
An electric current produced the deflection of a compass needle.
Another magnetic field than the Earth’s is affecting the needle
moving electric charges also create
magnetic field.
Moving charges can be found in
wires under electric current .
http://www.youtube.com/watch?v=q
wq54NMtDtA
http://ocw.mit.edu/courses/physics/8-02electricity-and-magnetism-spring2002/video-lectures/lecture-11-magneticfield-and-lorentz-force/
8.00
Electric current produces magnetic field!!!!!!!
Magnetic field of a current-carrying wire
We have a long current carrying wire. The current flow is 50 A. We
make a loop on the wire like on the graph with radius of 10 cm.
Straight wire: right-hand rule
I
B 0
2R
I
How big is the magnetic induction in the middle of the loop
R
B
Loop:
If the plane of the loop is perpendicular to the wire?
If the plane is paralell to the wire?
I
B  0
2R
I
Solenoid:
A coiled wire
= lots of loops
B  0
I N
l
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2012.03.26.
In a magnetic field:
From the same wire first we make a circle with the radius of R. Then
we double the loops and make a solenoid. The radius will be R/2.
In wich case do we have stronger magnetic induction and what is
the ratio of difference?
Place a linear wire in the magnetic field of a horseshoe magnet.
Switch current on the wire. The wire will move perpendicularly to the
induction lines of the magnetic field.
If we change the direction of the current than the movement’s
direction will change also in the opposite direction.
B
S
Direction of the movement
I
I
B  0
I
2R
B  0
I
I
 2  0  2
R
R
2
2
F
l
B
F
N
-
Force on wire under
current
 

F  I l  B
+
Lorentz force

 
F  qv  B
Force on a moving charge
In general (in case of a solenoid frame) we can determine
the moment of rotation:
The force acting on one
side of the frame is:
Torque:

The angle between the
solenoid frame and the
magnetic field direction
of the shoemagnet.
F  I l  B
http://ocw.mit.edu/courses/physics/8-02electricity-and-magnetism-spring2002/video-lectures/lecture-11-magneticfield-and-lorentz-force/
35.00; 9.30
M  F  d  sin 
M  B  I  l  d  sin   B  I  A  sin 
If we have more turns in our solenoid, the torque will change like this:
M  N  B  I  A  sin 
A  l d
F  I l  B

B
Magnetic induction
F
B
I l
Magnetic flux
  B A
Unit:
B  Vs2  T
m
tesla
Earth: 0,5 G
Fridgemagnets: 35–200 G,
Industry: 300–5000
MRI 200 000 G
In homogenous magnetic field the
magnetic flux is the number of the
induction lines passing through the
surface A perpendicular to the induction
lines.
  Vs  Tm2  W
weber
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2012.03.26.
Electromagnetic induction
If we move a wire in a magnetic field and it crosses
induction lines than electric potential can be measured
at the ends of the wire.
If we change the current on the left side than magnetic flux
will also change on the other side and electric potential can
be measured.
Fe
+
measure
S
Switch on and off
I
-
N
-
V
Direction of the movement
l
B
+
This phenomenon is called
electromagnetic
induction
and the measured potential is
called induced potencial.
Electric potential
No movement.
Lenz’s law
Electric potential is enduced in a wire if
- Intersection of the induction lines happens during
movement.
- Change of the magnetic flux in the surface
surrounded by the wire appears.
The direction of the potential enducing movement is opposite to the
direction of the movement enduced by the changing current.
The direction of the induced current is such that the magnetic
influence of it inhibits the inducing movement or changes.
S
S
B
B
Direction of the induced current (potential)
Flemings right hand rule!
B
l
F
l
I
I
N
I
Change of the magnetic flux.
N
moving
currentflow
+
+
"An induced current is always in such a direction as to oppose the motion or
change causing it"
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2012.03.26.
Self-induction
Magnitude of the induced potential
U  B l v

N
t
Neumann’s law: the induced potential is directly
proportional with magnetic induction, with the length of the
wire and the movements speed perpendicular to the
induction lines.
The induced electromotive force or
EMF in any closed circuit is
PROPORTIONAL to the time rate of
change of the magnetic flux through
the circuit.
If the current is changing in a conductor, the flux of the
conductor’s magnetic field will change too, which induces
potential in the conductor itself.

BA
s  N
N
N
t
t
The electromotive force is directly proportional to the change of
magnetic flux in by wire surrounded area and inverse proportional
with the time needed for the change.

IN
A
N 2 A I
I
l

 L
t
l t
t
L  Vs  H
A
H [ Henry] self-induction constant
Homework:
How large is the magnetic induction in a solenoid with
We make a solenoid from copper wire. The length of the
the following parameters?
solenoid is 30 cm, the number of turns is 2400. We
Number of turns is 1200, length 30 cm, diameter is 5 cm,
connect 60 V potential on it. The diameter of the WIRE is
and the current is 2 A.
0,3 mm and the length of one turn is 8 cm. The resistivity
What is the magnitude of the magnetic flux in the
of the copper is 0,017 Ω mm2/m.
solenoid?
How many ohm is the is the resistance of the wire?
How big is the magnetic induction of the solenoid if the
I N
B  0
l
  B A
inner is filled with air?
R
 l
A
I
U
R
B  
N I
l
6