Ampere"Magnetic Field Intensity":

meter

H

I

l

I H d

l

Amperes Law

I is the total current linking the magnetic flux. It may be N wires carrying I/N amperes.

l

lg

lm

Hg

Hm

N

i

I H d H H Ni

m ml lg gl

B H

BA HA

HA

Ni H HA A

g mg g

g g m m

l ll m ml

Ni g mR R R

A Ag m

Due to fringing in the gap.

Ni R

“Reluctance”

A

lg

lm

Hg

Hm

N

i

Flux Linkage: Total flux “linking” the conductor

2

m

N iN

R

2 volt second henry =

amperem N

Li

RDefinition of Inductance:

WebersBA HA Total Flux :

The Total Flux is the Total Flux, whether you’re talking about the flux in the magnetic material, or the flux in the gap.

2

weber Tesla =

meterB H

Magnetic field energy stored in an inductor is:

2 22

2 2 2

nI HLIW

l

R RVolume

Energy Density 3

J

m

2 2 2 2

2 21

2 2 2 2 2

H A H BA A

A

l

l l l Rl

Example: = 4 x 10-4 Webers of flux exists in a gapped magnetic core having cross sectional area of 1 cm2 and length 20 cm. The gap is 3 mm in length. Consider the cross sectional area of the gap to be 1.5 cm2 due to fringing. The core has = 103 0.

Determine the energy stored in the core and in the gap.

Determine the reluctance of the gapped core.

If the winding consists of 1000 turns, determine the current.

What is the inductance?

6 1

2 30

6 12

0

0.22.39 x 10 hy

.0001 10

0.00315.9 x 10 hy

.00015

c

g

m

m

m

m

R

R

26 1 4

26 1 4

2.39 x 10 hy 4 x 100.19

2

15.9 x 10 hy 4 x 101.27

2

c

g

wW J

wW J

6 118.29 x 10 hyT c g R R R

4 6 14x 10 18.29 x 10 hy7.3

1000T

wI A

N

R

22

6 1

1000.0547

18.29 x 10 hyT

NL hy

R