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# Notes - Magnetic Material Notes | EduRev

## : Notes - Magnetic Material Notes | EduRev

``` Page 1

Magnetic Materials
• The inductor
F
B
= LI (Q = CV)
1 ?B
?F
B
= L
?I
?×E = - (CGS) ?t ?t
?×EdS
c
=
?t
-
1 ?
( BdS )= -
1 ?F
V
EMF
= -
?N
?
F
t
B
= -L
?
?
I
t
??
c ?t
??
c ?t
B
?I ?V

F
B
= magnetic flux density V = L (recall I =C for the capacitor)

?t ?t
??
?×EdS =
?
E ·d l (Green's Theorem)
?I

Power =VI = LI

V =
?
E ·d l = -
1 ?F
B
(explicit Faraday's Law)
?t
c ?t
Energy =
?
Power ·dt =
?
LIdI =
1
LI
2
=
1
NF
B
I
2 2
?
1
2
?
?
capacitor CV
?
?
2
?
©1999 E.A. Fitzgerald
1
Page 2

Magnetic Materials
• The inductor
F
B
= LI (Q = CV)
1 ?B
?F
B
= L
?I
?×E = - (CGS) ?t ?t
?×EdS
c
=
?t
-
1 ?
( BdS )= -
1 ?F
V
EMF
= -
?N
?
F
t
B
= -L
?
?
I
t
??
c ?t
??
c ?t
B
?I ?V

F
B
= magnetic flux density V = L (recall I =C for the capacitor)

?t ?t
??
?×EdS =
?
E ·d l (Green's Theorem)
?I

Power =VI = LI

V =
?
E ·d l = -
1 ?F
B
(explicit Faraday's Law)
?t
c ?t
Energy =
?
Power ·dt =
?
LIdI =
1
LI
2
=
1
NF
B
I
2 2
?
1
2
?
?
capacitor CV
?
?
2
?
©1999 E.A. Fitzgerald
1
The Inductor

4p 1 ? E
?× B = J +
c c ? t
4p 4p
??
?× BdS =
?
B · d l =
??
J · dS = I
c c
4p
B = In
c
N = n · length = nl
Nf
B
N (BA) 4p
2
L = = = n lA
I I c
Insert magnetic material

Magnetic dipoles in material can line-up in magnetic field
B = H + 4p? H = H + 4p M
B magnetic induction
? M
? magnetic susceptibility
M = ?H = ? µ = 1+ 4p?
H magnetic field strength (applied field)
? H
M magnetization
B = 4pM + 1 B = µH
2
©1999 E.A. Fitzgerald
Page 3

Magnetic Materials
• The inductor
F
B
= LI (Q = CV)
1 ?B
?F
B
= L
?I
?×E = - (CGS) ?t ?t
?×EdS
c
=
?t
-
1 ?
( BdS )= -
1 ?F
V
EMF
= -
?N
?
F
t
B
= -L
?
?
I
t
??
c ?t
??
c ?t
B
?I ?V

F
B
= magnetic flux density V = L (recall I =C for the capacitor)

?t ?t
??
?×EdS =
?
E ·d l (Green's Theorem)
?I

Power =VI = LI

V =
?
E ·d l = -
1 ?F
B
(explicit Faraday's Law)
?t
c ?t
Energy =
?
Power ·dt =
?
LIdI =
1
LI
2
=
1
NF
B
I
2 2
?
1
2
?
?
capacitor CV
?
?
2
?
©1999 E.A. Fitzgerald
1
The Inductor

4p 1 ? E
?× B = J +
c c ? t
4p 4p
??
?× BdS =
?
B · d l =
??
J · dS = I
c c
4p
B = In
c
N = n · length = nl
Nf
B
N (BA) 4p
2
L = = = n lA
I I c
Insert magnetic material

Magnetic dipoles in material can line-up in magnetic field
B = H + 4p? H = H + 4p M
B magnetic induction
? M
? magnetic susceptibility
M = ?H = ? µ = 1+ 4p?
H magnetic field strength (applied field)
? H
M magnetization
B = 4pM + 1 B = µH
2
©1999 E.A. Fitzgerald
H and B

•	 H has the possibility of switching directions when leaving the material;
B is always continuous
3
©1999 E.A. Fitzgerald
p
q
H
B
At p:
At q:
B H
M=0
M
M
M
H
B
Page 4

Magnetic Materials
• The inductor
F
B
= LI (Q = CV)
1 ?B
?F
B
= L
?I
?×E = - (CGS) ?t ?t
?×EdS
c
=
?t
-
1 ?
( BdS )= -
1 ?F
V
EMF
= -
?N
?
F
t
B
= -L
?
?
I
t
??
c ?t
??
c ?t
B
?I ?V

F
B
= magnetic flux density V = L (recall I =C for the capacitor)

?t ?t
??
?×EdS =
?
E ·d l (Green's Theorem)
?I

Power =VI = LI

V =
?
E ·d l = -
1 ?F
B
(explicit Faraday's Law)
?t
c ?t
Energy =
?
Power ·dt =
?
LIdI =
1
LI
2
=
1
NF
B
I
2 2
?
1
2
?
?
capacitor CV
?
?
2
?
©1999 E.A. Fitzgerald
1
The Inductor

4p 1 ? E
?× B = J +
c c ? t
4p 4p
??
?× BdS =
?
B · d l =
??
J · dS = I
c c
4p
B = In
c
N = n · length = nl
Nf
B
N (BA) 4p
2
L = = = n lA
I I c
Insert magnetic material

Magnetic dipoles in material can line-up in magnetic field
B = H + 4p? H = H + 4p M
B magnetic induction
? M
? magnetic susceptibility
M = ?H = ? µ = 1+ 4p?
H magnetic field strength (applied field)
? H
M magnetization
B = 4pM + 1 B = µH
2
©1999 E.A. Fitzgerald
H and B

•	 H has the possibility of switching directions when leaving the material;
B is always continuous
3
©1999 E.A. Fitzgerald
p
q
H
B
At p:
At q:
B H
M=0
M
M
M
H
B
Maxwell and Magnetic Materials

•	 Ampere’s law
?
H · d l = I = 0
•	 For a permanent magnet, there is no real current
flow; if we use B, there is a need for a fictitious
current (magnetization current)
•	 Magnetic material inserted inside inductor
increases inductance
F
B
= BA ~ 4pMA = 4p?HA = 4p?
?
?
4p
In
?
?
A
?
c
?
NF
B
()
2
Material Type
?
4p
2
L = = n lA?
I c
Paramagnetic +10
-5
-10
-4
L increased by ~? due to
magnetic material
Diamagnetic -10
-8
-10
-5
Ferromagnetic +10
5
©1999 E.A. Fitzgerald
4
Page 5

Magnetic Materials
• The inductor
F
B
= LI (Q = CV)
1 ?B
?F
B
= L
?I
?×E = - (CGS) ?t ?t
?×EdS
c
=
?t
-
1 ?
( BdS )= -
1 ?F
V
EMF
= -
?N
?
F
t
B
= -L
?
?
I
t
??
c ?t
??
c ?t
B
?I ?V

F
B
= magnetic flux density V = L (recall I =C for the capacitor)

?t ?t
??
?×EdS =
?
E ·d l (Green's Theorem)
?I

Power =VI = LI

V =
?
E ·d l = -
1 ?F
B
(explicit Faraday's Law)
?t
c ?t
Energy =
?
Power ·dt =
?
LIdI =
1
LI
2
=
1
NF
B
I
2 2
?
1
2
?
?
capacitor CV
?
?
2
?
©1999 E.A. Fitzgerald
1
The Inductor

4p 1 ? E
?× B = J +
c c ? t
4p 4p
??
?× BdS =
?
B · d l =
??
J · dS = I
c c
4p
B = In
c
N = n · length = nl
Nf
B
N (BA) 4p
2
L = = = n lA
I I c
Insert magnetic material

Magnetic dipoles in material can line-up in magnetic field
B = H + 4p? H = H + 4p M
B magnetic induction
? M
? magnetic susceptibility
M = ?H = ? µ = 1+ 4p?
H magnetic field strength (applied field)
? H
M magnetization
B = 4pM + 1 B = µH
2
©1999 E.A. Fitzgerald
H and B

•	 H has the possibility of switching directions when leaving the material;
B is always continuous
3
©1999 E.A. Fitzgerald
p
q
H
B
At p:
At q:
B H
M=0
M
M
M
H
B
Maxwell and Magnetic Materials

•	 Ampere’s law
?
H · d l = I = 0
•	 For a permanent magnet, there is no real current
flow; if we use B, there is a need for a fictitious
current (magnetization current)
•	 Magnetic material inserted inside inductor
increases inductance
F
B
= BA ~ 4pMA = 4p?HA = 4p?
?
?
4p
In
?
?
A
?
c
?
NF
B
()
2
Material Type
?
4p
2
L = = n lA?
I c
Paramagnetic +10
-5
-10
-4
L increased by ~? due to
magnetic material
Diamagnetic -10
-8
-10
-5
Ferromagnetic +10
5
©1999 E.A. Fitzgerald
4
Microscopic Source of Magnetization
• No monopoles
• magnetic dipole comes from moving or spinning electrons
Orbital Angular Momentum

A
µ
µ is the magnetic dipole moment
r
r
Energy = E = -µ ·H = - µ H cos?
I
e-
L
What is µ? For ?=0,
E = -µH ˜ -F
B
I since energy ~ LI
2
and for 1loop L =
F
B
I
F
B
=
??
H ·dS ~ HA
?µH = F
B
I = HAI and ?µ = IA
I = -
e ?
A = pr
2
c 2p
µ = -
e
?r
2
2c
5
©1999 E.A. Fitzgerald
```
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