Laurea Magistralis
MEDICINE
and SURGERY
Corso di in
Laurea
Specialistica
in
MEDICINA
e CHIRURGIA
“HARVEY”
corso integrato
FISICA - disciplina
FISICA
Integrated
Course/Discipline:
PHYSICS
MAGNETIC FIELD
- CHARACTERISTICS OF THE MAGNETIC FIELD
- LORENTZ’S FORCE
- MAGNETIC MOMENT
- SOLENOID
- MAGNETIC PROPERTIES OF MATTER
- CIRCULATION THEOREM
D. SCANNICCHIO 2009
01/22
MAGNETIC FIELD
force
azionibetween
di forza wires
tra filiwhen
percorsi legge
Laplace’s
law
di Laplace
crossed
by anelettrica
electric:current:
da corrente
µ i1 i 2
Δl
F =
→
2π d
–F
i1
permeability
µ = magnetic
permeabilità
magnetica
Δl
d
→
+F
i2
F = B i2 Δl
leggeand
di Biot
e Savart
Biot
Savart’s
law
µ i1
B=
2π d
B = modulus of the magnetic induction vector
or magnetic field (produced by i1)
D. SCANNICCHIO 2009
02/22
MAGNETIC FIELD
legge
di Laplace
Laplace’s
law
y
o
z
i
x
→
→
→
F = Δl i2 ∧ B
magneticmagnetica
induction
induzione
→
B
→
B
modulus:
modulo :
leggeand
di Biot
e Savart
Biot
Savart’s
law
→
µ i1
B=
2π d
B
→
direction : ⊥ i
direzione
versus: rotazione
: rotation vite
of a screw→
verso
avanzante
verso
di i i
moving as
current
→
B
i
D. SCANNICCHIO 2009
B solenoidal field (closed line of force)
03/22
MAGNETIC FIELD
B solenoidal field (closed line of force)
L (closed path) ≠ 0
force field NOT CONSERVATIVE (in general)
dimensions: [B] =
[force]
= [M] [t]–1[Q]–1
[L] [electric current]
measure units:
newton
weber
volt
•s
=
=
= tesla (T)
I.S.
2
2
ampere • m
m
m
practice
gauss = 10–4 tesla
earth magnetic field: on ground ≈ 0.5 gauss
D. SCANNICCHIO 2009
04/22
MAGNETIC PERMEABILITY
µ i1 i2
Δl
F =
2π d
µ = µo µr
µ = permeabilità
magnetica
magnetic permeability
µo = 4 π 10–7 kg ⋅ m ⋅ C–2
µo = permeabilità
magnetica
nel vuoto
vacuum magnetic
permeability
magnetica
relativa
materia)
related magnetic
permeability
(in (nella
the matter)
µr = permeabilità
diamagnetiche
µr ~< 1 sostanze
diamagnetic
materials
paramagnetic
materials
µr >
paramagnetiche
~ 1 sostanze
ferromagnetic
materials
µr >>
˘ 1 sostanze
ferromagnetiche
D. SCANNICCHIO 2009
05/22
MAGNETIC FIELD INTENSITY
magnetic vector
vettore
magnetico
non
not dependent
from materials
dipendente dalla materia
→
B
H = µ
→
dimensions:
dimensioni
[M][t]–1[Q]–1
–1 –1
[L]
[t] [Q]
[H] =
=
–2
[L][M][Q]
D. SCANNICCHIO 2009
06/22
LORENZ’S FORCE
legge
di Laplace
Laplace’s
law
→
→
→
F = Δl i2 ∧ B
generale
iningeneral,
for a
per
q incharge
moto q
moving
→
→
→
F= qv∧B
D. SCANNICCHIO 2009
→
B
→
v
y
q
o
x
z
→
F
Lorentz’s
force
forza
di Lorentz
07/22
MAGNETIC MOMENT
spira
percorsa
corrente:
electric
current da
through
a coil
→
→
n
magnetic
moment
M definition:
momento
magnetico
M
→
i
→
M=iSn
→
M
S
measure units:
→
in a magnetic
field B :
in campo
magnetico
ampere • m2
I.S.
→
equilibrio : M
equilibrium
→
→
B
→
same behaviouridem
as a magnet:
calamita : nord = M
M
D. SCANNICCHIO 2009
08/22
MAGNETIC MOMENT
spira
percorsa
corrente:
electric
current da
through
a coil
→
→
momento moment
magnetico
n
magnetic
M :M
→
M=iSn
→
i
M
S
→
→
→
same behaviour
a magnet:
idem as
calamita
: nord = M
M
→
in a magnetic
field B :
in campo
magnetico
→
equilibrio : M
equilibrium
→
B
Ampère’s
principio
di equivalence
equivalenzaprinciple
di Ampère :
calamita
magnet
D. SCANNICCHIO 2009
≡ spira
percorsabyda
corrente
coil crossed
a current
09/22
SOLENOID
circular
coil :
spira
circolare
→
(B al
della
spira)coil)
atcentro
center of
circular
legge
di Savart’s
Biot e Savart
Biot
and
law
µ i1
B=
2π d
µi
B=
2R
D. SCANNICCHIO 2009
→
n
i
S
→
B
R
10/22
SOLENOID
solenoide
circolari)
solenoid (N
(N spire
circular
coils) :
→
B
→
N
i
campo
magnetico
uniforme
uniform
magnetic
field
n= N
l
D. SCANNICCHIO 2009
B
solenoid in
solenoide
longitudinal
in sezione
l longitudinale
section
B=µin
11/22
SOLENOIDAL FORCE FIELD
permanent
magnet
magneti
permanenti
N
N
S
→
B
→
B
S
→
S
B
S
D. SCANNICCHIO 2009
N
N
dipolo
magnetic
magnetico
dipole
12/22
MAGNETIC PROPERTIES OF MATTER
atomo
atom
atomic electron
orbitali
atomiciorbitals
microscopic
coils : :
spire
microscopiche
→
orbital magnetic
moment
m m
momento
magnetico
orbitale
→
momento
magnetico
dis spin s
spin magnetic
moment
proprietà
materialsmagnetiche
magnetic
dei
materiali
properties
D. SCANNICCHIO 2009
diamagnetismo
diamagnetism
paramagnetismo
paramagnetism
ferromagnetism
ferromagnetismo
13/22
MAGNETIC PROPERTIES OF MATTER
diamagnetismo
diamagnetism
(composticompounds)
organici)
µr <
1
(organic
~
→
→
m = 0 s = 0 (induzione magnetica)
(magnetic induction)
paramagnetismo
paramagnetism
→
→
m≠0 s ≠0
µr >
~1
(Mn2+, Cu2+, Fe3+ )
(orientamento
microscopico
medio)
(mean
microscopic
orientation)
ferromagnetismo µr >> 1 (Fe, Co, Ni )
ferromagnetism
→
→
m ≠ 0 s ≠ 0 (full macroscopic orientation)
(orientamento macroscopico completo)
µr = f(T)
D. SCANNICCHIO 2009
T > Tcurie ferro-
para-magnetismo
14/22
CIRCULATION THEOREM
i
y
o
z
x
→
dα
r
ds
B=µ
→
B
i
2π r
legge
e Savart
Biot di
andBiot
Savart’s
law
(circonferenza)
(circumference)
i
n
→
circuitazione
di B
circulation of
→
=∑ Bi Δsi =
→
i =1
→ →
⌠
⌠
= B ds =
⌡
⌡
(circumference)
(circonferenza)
D. SCANNICCHIO 2009
2π
⌠
µi
µ i dα =
ds =
2π r
⌡ 2π
0
15/22
CIRCULATION THEOREM
2π
µ i⌠
µi
dα =
=
2π ⌡
2π
α
2π
0
0
teorema
della circuitazione
circulation
theorem
(teorema di Ampère)
(Ampère’s theorem)
µ i 2π
=
=µi
2π
→
⌠ B→ ds
⌡
=µi
general validity (line connected to the circuit)
validità generale (linea concatenata al circuito)
conseguenza
:
consequences:
→
B not
non conservative
conservativo
(see #17)
D. SCANNICCHIO 2009
16/22
B NOT CONSERVATIVE
forza
non conservativa
not conservative
force: :
⌠
⌡
dL
→ →
⌠
= F ds
⌡
≠0
proprietà matematica
mathematical
property generalizzabile
generalizable to
a any
qualsiasi
solo to
alle
forze
kind ofvettore,
vectorsnon
not only
forces
→
⌠ X→ ds
⌡
≠0
→
vector X non
not conservative
vettore
conservativo
teorema della circuitazione
circulation theorem:
conseguenza :
consequence
→
→
⌠
⌡
B ds = µ i
D. SCANNICCHIO 2009
→
B not
non conservative
conservativo
17/22
CIRCULATION THEOREM
linea
NON connected
concatenatatoalthe
circuito
line NOT
circuit
VUOTO
VACUUM
i
r2
r1
→
→
→
.
B AB = – B. →
CD
→ →
→ →
B . DA = B. BC = 0
C
α
B
D
→
⌠ B→ ds
⌡
l
A
y
o
z
x
=0
materia
: linee
chiuse
in matter:
closed
linessempre
always concatenate
connected to
alcircuit
circuito(atomic
(microspire
atomiche)
micro-coils)
in vacuum: closed lines without currents
D. SCANNICCHIO 2009
18/22
LORENZ’S FORCE EFFECTS
→
→
:
case
lar
particu
uniform , ⊥ v
caso
particolare
: B uniforme
→
B:
→
B
R
.
→
→
v
F
+q
ingoing
uscente
outgoing
entrante
dv
FT = m aT = m
=0
dt
2
m
v
FN = m aN =
=qvB
R
motion
uniformuniforme
circular
moto
circolare
D. SCANNICCHIO 2009
19/22
LORENZ’S FORCE EFFECTS
FT = m aT = m dv = 0
dt
2
m
v
FN = m aN =
=qvB
R
L = ΔTEk== 00
mv
R=
qB
q
v
2
π
ω=
=
=m B
R
T
q
di m
ement of
measurmisura
D. SCANNICCHIO 2009
20/22
LORENZ’S FORCE EFFECTS
→
→
:
case: B uniforme, v general
in generale
generico
general
ry
spiral trajecto
traiettoria
elicoidale
→
v⊥
q
y
z
o
D. SCANNICCHIO 2009
→
v
→
v ⁄⁄
x
21/22
LORENZ’S FORCE EFFECTS
→
forzaLorentz
di Lorentz
’s force
→
→
F= qv∧B
→
in generale seinpresente
un campo
elettrico
field E :
an electric
present
general ifanche
→
→
→
→
F = qE + q v ∧ B
velocitydiselector
selettore
velocità
→
F
→
+
–
D. SCANNICCHIO 2009
F=qE–qvB=0
B
+
v>E
B
E
v
=
→
+q
B
E
–
v<E
B
22/22