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