Transcript Production of induced force on a wire

Magnetic Field
Basic Concepts:
A current carrying wire produces a magnetic field
in the area around it.
A time changing magnetic field induces a voltage in a
coil (wire) if is passes through the coil (transformer)
A moving wire in the presence of a magnetic field has a
voltage induced in it (generator)
A current-carrying wire in the presence of a magnetic
field has a force induced on it (motor).
Faraday’s Law- Induced voltage from a
time-varying magnetic field
Faraday’s Law for a single wire
eind
d

dt
Faraday’s Law for a coil
d
eind   N
dt
If we define, : 
Then we have:
 N
Flux linkage
eind
d

dt
Ideal Transformer
d
vp  N p
dt
vs N s

vp N p
d
vs  N s
dt
is N p

ip N s
Self and Mutual Inductance
In a coil
d d
e
 N
dt dt
d F d N .i
 N  N
dt  dt 
N 2 di
di

L
 dt
dt
N2
L

In a transformer
Lp 
Np
2

2
Ns
Ls 

NsN p
M

Production of induced force on a
wire
F  i ( l  B)
F  ilB sin 
if   90
F  ilB
Direction of l is the same as i
Vector Product
z  x y
Induced voltage on a conductor
moving in a magnetic field
eind  (V  B).l
eind  VBl sin 1 cos 2
if 1  90 and 2  0
eind  VBl
Direction of l is such that it would make the smallest angle with (V B)
The positive side of the resulted voltage in where (V B) points
How much do you think the induced voltage is?
AC excitation of magnetic
circuits
What do we mean by AC excitation?
1- Inserting sinusoid current (what we have considered so far)
2- Applying sinusoid voltage
Q: What happens if we somehow insert sinusoid current to a coil?
Will the flux and induced voltage be sinusoid as well?
A: No, because of saturation and hysteresis
Q: What happens if we apply sinusoid voltage to a coil? Will the flux
and current (magnetizing current) be sinusoid as well?
A: No, because of saturation and hysteresis
Conclusion: In a coil current and voltage cannot be sinusoid
simultaneously. If one is sinusoid, the other is not.
Let’s see what would happen if we apply
sinusoid voltage to a coil?
d
eN
dt
e  Vm . cost
1
   Vm . costdt
N
Vm

. sin t
N .
Magnetization current