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

dt

deind

dt

dNeind

Faraday’s Law for a single wire

Faraday’s Law for a coil

If we define, :Then we have:

Flux linkage

N

dt

deind

Ideal Transformer

dt

dNv pp

dt

dNv ss

p

s

p

s

N

N

v

v

s

p

p

s

N

N

i

i

Self and Mutual Inductance

2

2

.

NL

dt

diL

dt

diN

iNN

dt

dFN

dt

d

Ndt

d

dt

de

ps

ss

pp

NNM

NL

NL

2

2

In a coil In a transformer

Production of induced force on a wire

ilBF

if

ilBF

iF

90

sin

)(

Bl

Direction of l is the same as i

Vector Product

yxz

Induced voltage on a conductor moving in a magnetic field

VBle

andif

VBle

e

ind

ind

ind

0 90

cossin

21

21

B).l(V

Direction of l is such that it would make the smallest angle with B)(V

The positive side of the resulted voltage in where B)(V 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.

tN

V

tdtVN

tVedt

dNe

m

m

m

sin..

cos.1

cos.

Let’s see what would happen if we apply sinusoid voltage to a coil?

Magnetization current