This document discusses magnetic circuits containing permanent magnets. It defines a magnetic circuit as a closed path traced by magnetic lines of force or flux. Circuits containing permanent magnets that generate magnetic flux in a closed path are the topic. These circuits can be analyzed using Ampere's Circuital Law, where the magnetic flux through any closed surface is zero. Reluctance, which is the opposition to magnetic flux in a circuit, is introduced and explained for parts made of soft iron and air gaps.

2. TOPIC
MAGNETIC CIRCUITS
CONTAINING PERMANENT
MAGNETS
PRESENTED BY:
ZERMEEN FATIMA
(ROLL#08)

3. PERMANENT MAGNETS
Brief Introduction:
• What are they made up of?
Ferromagnetic materials (iron, nickel, or alloys made up of rare earth
metals)
• What is Ferromagnetism?
The magnetic domains cause ferromagnetism.

5. MAGNETIC CIRCUITS
• Magnetic circuit is defined simply as the closed path traced by
magnetic lines of force or magnetic flux.

6. • Circuits made up by using a ferro-magnet or permanent magnet that
generates a magnetic flux in a closed path is our topic of discussion
today…
• In more simple words: Flux circuits in which has its origin in
permanently magnetized material.

7. • We will apply Ampere Circuital Law to the flux path of PM circuit.
Permanent Magnet: PM

8. Lets start:
𝑯. 𝒅𝒍 = 𝑰 The magnetic flux though any closed surface is zero. So:
• For the path a to b :
𝑯. 𝒅𝒍 = 𝟎

9. Using 𝑩 = 𝝁𝑯 we have:
𝑯 =
𝑩
𝝁
&
Using ∅ = 𝑩𝑨 we have:
𝑩 =
∅
𝑨
So 𝑯 =
∅
𝑨𝝁
Putting this value in

10. Putting 𝑯 =
∅
𝑨𝝁
in above we have:

11. LHS
• As magnetic flux Ø is continuous
through out the circuit so
Ø= BmAm
Where: Bm = magnetic field in permanent
magnet
Am = cross-sectional area of permanent
magnet
So:
BmAm
RHS
• Can be written as –Hmlm
Where: Hm= average magnetic intensity in
magnet
Lm= length of the magnet
So:
–Hmlm

12. RELUCTANCE
• So this eq after putting all the values, finally becomes:
Explained in next
slide….
Values of Bm and
Hm can be
calculated by
hysteresis curve of
the magnet

13. What is Reluctance

14. Reluctance
• Air gap
• Soft iron having negligible
hysteresis as it is not a PM.
• The air gap in magnetic circuit means the magnetic
resistance i.e. reluctance to the magnetic flux
density. This can be reduced by increasing the size
of PM.
• Reluctance is the opposite phenomenon of
Permeability.

15. • So Reluctance
=
Subscript i
is for SOFT
IRON
Subscript
g is for
AIR GAP

16. 0So Reluctance is reduced to:

17. 𝑩 𝒎 𝑨 𝒎 = −𝑯 𝒎 𝒍 𝒎

18. • For the value of Bm
𝑩 𝒎 𝑨 𝒎 = −𝑯 𝒎 𝒍 𝒎

19. For this calculation following approximations
are made:
1. Leakage flux is neglected.
2. Ag is taken equal to the pole face area.

20. Finally we head to the RESULT

21. • Magnetic intensity Hm in
the magnet is
DEMAGNETIZATION
EFFECT.
• When the magnetic flux has
its origin in the Permanent
magnet then the magnet
itself is subjected to a
demagnetization field.

22. Fun Fact
He can generate and manipulate magnetic fields. His powers allow him to
control metal, levitate himself and others, create force fields, use telepathic
mind control, and generate electromagnetic pulses.

24. THANK YOU