Magnetism, electromagnetic
induction, alternate current
Talián Csaba Gábor
PTE Med. School Inst. of Biophysics
06.11.2014.
Empirical knowledge
•
Some iron ores attract other metal
pieces
•
China
–
–
e g. magnetite (Fe2+Fe23+O4)
–
–
Earth-divining (→ Feng-shui)
How many needles can it lift →
quality categories
Moving magnets always take one direction:
navigation, difference of magnetic and
astronomic Earth poles
VII-X. century: compass
Magnesia, Greek city in Asia Minor
•
England, ~ 1600
Earth is a big magnet
William Gilbert
(1544-1603, ENG)
•
Natural magnetic property can be transmitted to another steel object by touch (artificial
magnet)
•
Magnet rod attracts other objects with its ends the most, barely with its middle part
magnetic poles (pointlike impact centers),
magnetic axis
(Poles from the end of the rod ~ 1/12 distance)
•
Magnet freely rotating around an axis takes always the same direction
→
the poles are unlike („positive” and „negative”)
•
Unlike poles attract, like poles repel one another
repulsion
attraction
•
Two magnets positioned with their
unlike poles cancel each other
repulsion
Magnetic influence
•
Softh iron
temporary magnet
•
Steel
permanent magnet
•
Magnet is like electric dipoles
magnetic momentum:
m = p*l
(p: pole strength; an analogon to electric charge, a quantity proportional to the
force/effect exerted by the magnet)
•
•
By division new dipoles can be made
The strength of the new pole equals the original one
Elementary, separable magnetic monopoles, „charges” do not exist
(theoretically predicted, but not found)
•
A metal rod contains many unoriented elementary magnets
that cancel the effect of the others
they can become oriented by an outer magnetic impact
like a chain of electric dipoles
orientation can remain or leave off
+
-
+
-
+
-
Magnetic force
•
Model of the „magnetic charge”: one end of a very long and thin magnet rod
~ Coulomb’s law:
= ∙
∙ = ∙
∙ ∙ p1, p2: magnetic pole strength, measure: V*s
r: distance(vector)
10 ∙ 1
=
=
(4 ∙ ) ∙ 4 ∙ ∙ = 1,257 ∙ 10
∙
∙
(induction constant, permeability)
Magnetic field
•
Every moving charged particle creates a magnetic field
In an unorganized physical body they cancel each other
•
Magnetic field (force) exerts torque on other magnets in it:
If a magnetic dipole stands in the direction of the outer magnetic then Mf = 0,
so it gives the direction of the field at that place
•
Magnetic field lines
run from the northern to the southern pole
Magnetic field strength points in a tangential direction of the field lines
•
Magnetic field strength I.
!"
=
#
H=
!$
%
(A/m)
Magnetic field strength II.
(magnetic inducion vector )
(induction density):
B
Measure: Tesla
(Vs/m2 = N/Am = 104 Gauss)
Nicola Tesla
(1856-1943, SRB-USA)
Magnetic field of the electric current
•
Strong direct current through a conductor makes the compass needle turn (Ørsted, 1820)
–
–
–
–
Electric current creates a magnetic field (Ampere’s law)
Every moving charge in general
Every substance has its magnetic field
Reverting the direction of the current the
shift of the pointer is opposite
Hans Christian Ørsted
(1777-1851, DEN)
Nearly homogenous magnetic fields
& = '
2π
)'
& *
'
& 2
& )'
2
North
északi
pole
pólus
I
Righ hand rule
Effect of the magnetic field on conductors
•
•
On conductors carrying current a force is acting in a magnetic field
Proportional to the angle between the direction of the current and the magnetic field
strength (ϕ)
'*&+,-
./ '01&+,-
1. EXERCISE: MAGNETIC FIELD OF THE ELECTRIC CURRENT
In a coil the number of turns is 13, the distance betwen them is 0,4 cm. A wire
frame of 8 cm edge length is located in the coil, parallel to the longitudinal axis.
If 1,5 A current is coupled on both the coil and the frame, what is the torque
acting on the frame?
)'
& *
& 1,257 ∙ 10
∙ 13 ∙ 1,5
∙
5,1 ∙ 104 5
∙ 0,048
./ '01&+,-
./ 1,5 ∙ 0,08
∙ 5,1 ∙ 104 5 4,9 ∙ 10 ) ∙ & = '
2
' *&
Modern definition of current(1948)
' ' *
2
Effect of the magnetic field on moving charges
•
Lorentz’s force:
= 7[9:]
An opposite direction on negative charges!
Hendrik Lorentz
(1853-1928, NED)
B and v perpendicular
not perpendicular
Devices working by the magnetic effect of
current
•
Galvanometer
DC
Ammeter with a turning coil
also AC
Electrodynameter
also AC
•
Electromagnet
•
Electric bell
Loudspeaker
Relay and interrupter
Cathode ray tube, television
Mass spectrometer
Electronmicroscope
2. EXERCISE: LORENTZ’S FORCE
What is the radius of orbit of an electron accelerated to 1 eV kinetic energy in
a magnetic field perpendicular to its direction of movement, if the magnetic
field strength is 0,5 T? The mass of the electron is 9,11·10-31 kg.
∙ <
7∙<∙& ∙<
7∙&
< 5,93 ∙ 10=
9,11·10−31 kg ∙ 5,93 ∙ 10= 6,75 ∙ 10 ?
1,6 ∙ 10 ∙ 0,55
Electromagnetic induction
•
Motional induction: relative displacement of a conductor in a magnetic field induces
electric current in the conductor
•
Conductional induction: magnetic field strength is chanching around a conductor
•
•
Magnetic flux passing the area around the conductor is changing in time
Voltage (current) is proportional to the rate of the change:
@ &*<
@ AΦ⁄AC A&⁄AC
•
Lenz’s law : direction of the induced current is so that it
impedes the effect that causes it
Heinrich Lenz
(1804-1865, GER)
Alternate current
•
Loop or coil rotated in a homogenous magnetic field
@ @EFG sin HC
@I// @EFG / 2
•
Modern generator
rotating magnet, voltage is generated on the stator
•
Electric motor: works in an inverted principle:
Current is coupled on the conductor in a magnetic field so it comes into motion
Serial RLC circuit
•
•
•
Ohmic resistance: the same against alternate current as direct current
Self-inducing coil: higher resistivity against alternate current proportionally to
inductivity ‚L’ and frequence ‚f’
Capacitor: lower resistivity against alternate current proportionally to
capacitance ‚C’ and frequence ‚f’
@ J' + L
M
A' 7
+
AC J + (LH −
Impedance
1 )
H
HOMEWORK
What is the effective voltage of the electric motor whose square-shaped
rotor has 30 cm as length and it makes 12.000 revolutions per minute in a
magnetic field of 0,25 T strength?
H =2∙∙S =
* 0,3 → = 0,15
<PFQR = ∙ H = 0,15 ∙ 1256
@EFG
1
2 ∙ ∙ 12000 +,
1
= 188,4
= & ∙ * ∙ < = 0,255 ∙ 0,3 ∙ 188,4 = 14,13
@I// =
@EFG
2
=
14,13
= 10
1,414
60
1
= 1256