Download Electromagnetism

Electromagnetism
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The magnetic field is described by the vectorial field B
[N / A m = Tesla = T]
Electric currents generates magnetic fields.
The magnetic field induced by an electric current flowing through an straight wire of infinite length is
µ·i
B=
2πd
B magnetic field induced by the wire (are concentrical circles centred in the wire and orthogonal to it). The direction
� is given by the right hand rule. d distance between the
of B
wire and the point on which the magnetic field is calculated.
Magnetic field in the centre of a wire loop
nµ · i
B=
2R
B magnetic field generated by the current i flowing through
a wire loop with n windings of radius R, calculated in the
centre of the wire loop.
R)
Magnetic field in the centre of a rectilinear solenoid (l �
nµ · i
B=
l
B magnetic field generated by the current i flowing through
the solenoid of length l.
Ferromagnetism
A ferromagnetic material is composed by microscopic magnets
(<<1 mm) generated by the motion of electrons in the atomic
orbitals which act as tiny wire loops
As a consequence of a sufficiently strong magnetic field the tiny
magnetic areas can be orientated conformally, amplifying of
several order of magnitudes the resulting magnetic field. If the
external magnetic field is sufficiently strong the small magnetic
areas can be orientated conformally in a permanent way. This
generated a magnet.
Electric motor
A simple DC (Direct
Current) motor. As the
current flows in the loops, a
magnetic field is generated
around the rotor. The left
side of the rotor is repulsed
by the left magnet while the
right side is attracted by the
right magnet. This generate
a torsion.
The rotor
continue to
rotate by inertia
As the rotor is horizontal
a commutator inverts the
direction of the current
through the wire loops,
modifying the polarity of
the induced magnetic
field. The process is thus
again in the initial state
and the cycles starts over.
The AC motor works without commutator since the inversion of polarity of the magnet is given
by the inversion on the current direction
Magnetic force (Lorentz’s force)
|F | = q · v · B · sin θ
F Force generated by a magnetic field on a charged particle
(e.g. electrons) in motion. q, �v = charge and velocity of the
� magnetic field. Lorenz’s Force F has direction
particle. B
�
perpendicular to the plane containing the vectors �v and B,
and is direction is given by the right hand rule.
Force applied on a segment of rectilinear wire of length l
containing a current i by an external magnetic field B with
angle θ w.r.t. l
F = i · l · B · sin θ
Galvanometro
corrente elettrica
da misurare
molla di richiamo
Mass spectrometer
A particle of charge q and mass m in motion on an uniform magnetic field B perpendicular to the velocity v, undertakes a circular trajectory of ridius r = m·v
q·B and angular
q
velocity ω = m
B.
Magnetic flow
θ
The flow of an homogeneous magnetic field B through
a surface S whose normal direction forms an angle θ w.r.t.
the direction of the magnetic field is:
ΦB = B · S · cos θ
Electromotive force (electric potential) induced � in a
circuit by the variation of magnetic flux ∆ΦB concatenated
to the circuit in a time interval ∆t
∆ΦB
�=−
∆t
the minus sign denotes the fact that the induced current is
in opposition to the variation of the magnetic field ∆ΦB .
Electric generator behavior opposite to the electric motor
θ