e&m-traccia 15
TRANSCRIPT
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( )( )
( )
( ) ( )
( )
( )
0
0
0 0
0 0 0
0
0
11
11
1
1
11
1
m
m
m
m
m m
m
m
m
m
m
m
m
n nc
n c
cn n
nc nc nc
nc
nc
χµχ
χχ µ
χ χχ
χ µ µ
µ µ µ
χ
χµχ
χµ
χ
= =
→ == ++
→ =+
= + → − =
+→ = = =
−−
+
≪ ≃
M μ B
M B
M H M M H
M H H H
M H
P o l a r i z z a b i l i t a ' m a g n e t i c a
S i n o t i :
R e l a z i o n e p i u ' s e m p l i c e : q u e l l a f r a
e
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( )
0
0
0
0 0
0
0
0
11 1
1
Vuoto:
Materia:
Definizione:
sempre
materiali omogenei, lineari, isotropi
relazione costitutiva mater
iali om
lib
lib m
m r
m r
r
µ
µ
µ
χ µ
µ χ µ µ
µ µ
∇⋅ =∇× = ∇⋅ =∇× = +
= −
−= =
+
→ =
B
B j
B
B j j
BH M
M B B
B H
0
ogenei, lineari, isotropi
equazioni della magnetostatica nei mezzi mater ialilib
∇⋅ =→∇× =
B
H j
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( ) ( )
0 0
,
libj H H
H r r
= →∇× =
→ =−∇Φ Φ
Osservazione interessante: in assenza di correnti libere
irrotazionale
potenziale magnetosta
tico
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Per dissipare un equivoco potenziale: Nell’esempio non ci sono correnti vere, tuttavia H e’ diverso da 0! Come mai? Nulla di strano: l’assenza di correnti vere determina solo
Ma un campo vettoriale non e’ determinato dal solo rotore: in generale riceve contributi anche dalla divergenza (vedi eq. di Maxwell) Quindi non c’e’ contraddizione fra assenza di correnti vere e campo H non nullo: disomogeneita’ in M agiscono come sorgenti di H. Infatti:
0
Quindi: 0 0
µ
∇ ⋅ = ∇ ⋅ − = −∇ ⋅
∇ ⋅ ≠ → ∇ ⋅ ≠
BH M M
M H
0H∇× =
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B
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ρlib
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