[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
MAGNETISM AND
Name: ______________________________
Section: ___________
ELECROMAGNETISM

Magnets attracts magnetic materials
but not non-magnetic materials. Magnetism is a non contact force (acts at a distance)
MAGNETISM

The ability to attract iron and steel. The knowledge of magnetism goes back to the
Ancient Greeks who realized that a certain rock (Iodestone) attracted pieces of iron.
When the hang a piece of this material, it rotates until it is pointing in a north-south
direction of the earth.

Magnets are named after the town magnesia (a district in Thessaly) in Lydia, Asia Minor
where the Iodestone was mined in ancient times. Natural permanents were called
Lodestone (magnetic,
Fe3
O4 ) after Iodestar (or guiding star). Lodestone was first
permanent magnetic material to be identified and studied. The regions near the ends of a
magnet are called its poles.
Magnetic Materials:

Iron

Steel
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)

Nickel

Cobalt
CLASSIFICATION OF MATTER ACCORDING TO THE MAGNETIC
PROPERTY
1. Ferromagnetic
If materials such as cobalt, nickel or iron are put near a magnet they begin to act like
another magnet. These substances when placed in a magnetic field are strongly
magnetized in the direction of the field. They are strongly attracted by a magnet. No
liquid is ferromagnetic.
Ferromagnetic materials are characterized by spontaneous magnetism that exists in
the absence of a magnetic field. They can retain the ability to attract metals
(particularly those belonging to ferrous family) even after the magnetic field that
induced magnetism to it has been removed. Iron is a soft ferromagnetic material. This
means it will become magnetized very easily, but quickly loses its magnetic
properties if the magnetized force is removed. Steel is more difficult to magnetize, but
once it is magnetized, it retains its magnetic properties for a long time. Steel is called
a “hard” ferromagnetic material.
2. Diamagnetic

Have the ability to slightly repel magnetic field. Faraday discovers these materials in
1845. He found that bismuth and glass are repelled from magnetic fields. These
substances when placed in a magnetic field acquire feeble magnetism opposite to the
direction of the magnetic field.
3. Paramagnetic

Also discovered by Faraday. He noted that some substances clearly not permanent
magnets are nevertheless attracted by magnetic fields and these materials are named
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)

paramagnetic. These substances when placed in a magnetic field, acquire feeble
magnetism in the direction of the magnetic field. They are feebly attracted by a
magnet.
MAGNET

A magnet is any object that has a magnetic field. It attracts ferrous objects like pieces of
iron, steel, nickel and cobalt. One of the most common magnets - the bar magnet - is a
long, rectangular bar of uniform cross-section that
attracts pieces of ferrous objects. The magnetic
compass needle is also commonly used. The
compass needle is a tiny magnet which is free to
move horizontally on a pivot. One end of the
compass needle points in the North direction and
the other end points in the South direction.
The end of a freely pivoted magnet will always
point in the North-South direction. The end that points in the North is called the North
Pole of the magnet and the end that points South is called the South Pole of the magnet. It
has been proven by experiments that like magnetic poles repel each other whereas unlike
poles attract each other.
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
The region around a magnet where a magnetic force can be felt is called the magnetic
field.
The magnet field is strongest at the poles of a magnet.

Like poles repel

Unlike poles attract
MAGNETIC FIELD
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)

Magnetic field is the space surrounding a magnet, in which magnetic force is exerted. If a
bar magnet is placed in such a field, it will experience magnetic force. However, the field
will continue to exist even if the magnet is removed. The direction of magnetic field at a
point is the direction of the resultant force acting on a hypothetical North Pole placed at
that point.
A magnetic field around a bar magnet has a shape and direction. The magnetic field is
represented using magnetic field lines (lines of force , flux lines) that show the shape, direction
and strength of the field.
HOW IS A MAGNETIC FIELD CREATED?

When current flows in a wire, a magnetic field is created around the wire. From this it
has been inferred that magnetic fields are produced by the motion of electrical charges. A
magnetic field of a bar magnet thus results from the motion of negatively charged
electrons in the magnet.

Magnetic fields are produced by electric currents, which can be macroscopic currents in
wires, or microscopic currents associated with electrons in atomic orbits. The magnetic
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
field (β) is defined in terms of force on moving charge in the Lorentz force law. The
interaction of magnetic field with charge leads to many practical applications. Magnetic
field sources are essentially dipolar in nature, having a north and south magnetic pole.
MAGNETIC FLUX DENSITY/FLUX DENSITY (β)

It is given by the flux passing per unit area through a plane at right angles to the flux. It is
measured in Wb/ m2
β=
Φ
A
= µH = µ 0
µr H
Φ
A
Direction of the magnetic field at any point is defined as the direction of motion of a change
particle on which the magnetic field would not exert force.
Magnitude of the magnetic field vector is proportional to the force acting on the moving charge,
the magnitude of its velocity and the angle between velocity and magnetic field. Unit is the Tesla
or Gauss
SI
Wb/ m 2 (Tesla)
CGS
Max/ cm 2 (Gauss)
ENG
lines/ ¿2
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
FLUX PER UNIT POLE OR MAGNETIC LINES OF FORCE

Just as an electric field is described by drawing the electric lines of force, in the same
way, a magnetic field is described by drawing the magnetic lines of force. When a small
north magnetic pole is placed in the magnetic field created by a magnet, it will experience
a force. And if the North Pole is free, it will move under the influence of magnetic field.
The path traced by a North magnetic pole free to move under the influence of a magnetic
field is called a magnetic line of force. In other words, the magnetic lines of force are the
lines drawn in a magnetic field along which a north magnetic pole would move.
The direction of a magnetic line of force at any point gives the direction of the magnetic
force on a north pole placed at that point. Since the direction of magnetic line of force is
the direction of force on a North Pole, so the magnetic lines of force always begin on the
N-pole of a magnet and end on the S-pole of the magnet. A small magnetic compass
when moved along a line of force always sets itself along the line tangential to it. So, a
line drawn from the South Pole of the compass to its North Pole indicates the direction of
the magnetic field.
PROPERTIES OF THE MAGNETIC LINES OF FORCE

The magnetic lines of force originate from the North Pole of a magnet and end at its
South Pole.

The magnetic lines of force come closer to one another near the poles of a magnet but
they are widely separated at other places.

The magnetic lines of force do not intersect (or cross) one another.
When a magnetic compass is placed at different points on a magnetic line of force, it aligns itself
along the tangent to the line of force at that point.
Magnetic Flux (φ) - It is the number of magnetic lines of forces in a magnetic field.
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)

Maxwell-unit of magnetic flux equal to one line of force. Named after the Scottish
physicist, James Clerk Maxwell (1831-1879)

Weber- SI unit of magnetic flux equal to
8
10
lines or Maxwell. Named after the
German physicist, Wilhelm Weber (1804-1891).
Conversion:
q = 1.602x 10−19 C 1 kg f = 9.81 N
1 N = 105 Dynes
1Wb = 1.256 gilberts
4
8
lb
1
= 4.4484 N 1 Tesla = 10 Gauss 1Wb = 1x 10 Maxwell
f
ABSOLUTE AND RELATIVE PERMEABILITY OF A MEDIUM

Permeability - the ability of a material to conduct magnetic flux through it.

Relative Permeability - ratio of the permeability of material to the permeability of air or
vacuum.
The phenomena of magnetism and electromagnetism are dependent upon a certain property of
the medium called its permeability. Every medium is supposed to possess two permeabilities:
µo

Absolute permeability,

Relative permeability, µ r
For measuring relative permeability, vacuum or free space is chose as the reference
medium. It is allotted an absolute permeability of vacuum with reference to itself is unity.
Hence, for free space,
Absolute permeability,
µ o = 4πx 107 Henry/meter, constant 33
Relative permeability, µ r = 1
Now, take any medium other than vacuum. If its relative permeability, as compared to
vacuum is µ r , then its absolute permeability is µ = µ o = µ r
MAGNETISING FIELD STRENGTH/FORCE/MAGNETIC INTENSITY (H)
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)

Field strength at any point within a magnetic field is numerically equal to the force
experienced by a N-pole of one Weber placed at that point.

It should be noted that the field strength is a vector quantity having both magnitude and
direction.

mmf (magnetomotiveforce) per unit length of path of the magnetic flux. It is also called
as the magnetizing force or the magnetic gradient

OERSTED - cgs unit of magnetic field strength equal to gilbert per centimeter.
AT/m – SI unit for H
1 oersted = 79.577 AT/m
H=
0.4 πNI
l
where:
H = magnetic field intensity(oersted)
l = mean length of path of the magnetic flux(cm)
T= magnetomotive force (gilbert)
MAGNETOMOTIVE FORCE OR MMF

Magnetomotive force is the force that sets up or tends to set up magnetic flux in a
magnetic circuit by passing an electric current through a number of turns of a wire.
where:
T = mmf ( ampere-turn)
T= NI
N = number of turns
I = current carried (ampere)
a. Long Straight Wire
¿
H = 2 πr
where: r = distance
N- Number of turns
Note…….
Gilbert – cgs unit of
magnetomotive force. Named
after the English physician and
physicist, William Gilbert.
T=
0.4�NI
I – Current in Amperes (A)
b. Long Solenoid
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
H=
¿
l
c. Circular Coil
where:
T = mmf ( ampere-turn)
N = number of turns
I = current carried (ampere)
¿
H = 2r
where: r – radius
d. Square Coil
H=
√ 2∋ ¿
πa
where: a – distance from the corner
¿
SAMPLE PROBLEMS
1. A solenoid 30 cm long is wound with 300 turns. What is the value of its field strength
inside the solenoid, when the coil is carrying a current of 2 Amperes?( In SI units)
2. If a current of 5A flows through a long wire of radius 0.004 meter, what is the intensity of
magnetic field produced 0.02 meter away from the surface of the wire?
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
MAGNETIC FORCES
FORCE ON A CHARGE

The amount of attraction or repulsion between charged objects can be put in quantitative
terms by the introduction of the electric force. The simplest case to consider is the force
between two points charges (charges with a negligible size)
F = qvβsinƟ (N)
where:
q – charge in Coulomb
Ɵ – angle between wire and magnetic field
v – velocity in m/s
β – flux density in Tesla
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
FORCE ON A CURRENT CARRYING CONDUCTOR LYING IN A MAGNETIC
FIELD

The magnetic force on a charged particle depends on the relative orientation of the
particle's velocity and the magnetic field.

A magnetic force cannot change the speed of a charged particle, only its direction.

When a charged particle enters a uniform magnetic field in a direction perpendicular to
that field, its motion is continuously changed by the magnetic force

A current consists of many small charged particles running through a wire. If immersed in
a magnetic field, the particles will be experience a force; they can transmit this force to
the wire through which they travel.

The force on a section of wire of length L carrying a current I through a magnetic field B
is
F = βILsinƟ
(N)
where:
β – Tesla
I – Current in Ampere (A)
L – length in meter (m)
F=
βILsinƟ
10
(Dynes)
where:
β – Gauss
I – Current in Ampere (A)
L – length in centimeter (cm)
F=
βILsinƟ
6
11.3 x 10
( lbf )
where:
β – lines
I – Current in Ampere (A)
L – length in in/ft
Because forces are easy to measure, it is the force exerted on a current-carrying wire which is
used to define the SI unit of current, the ampere.
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
FORCE BETWEEN TWO PARALLEL CONDUCTORS

Current in the same direction. The field strength in the space between the conductors is
decreased due to the two fields there being in the opposition to each other. Hence, the two
conductors are attached towards each other.

Current in the opposite direction. The field strength is increased in the space between
the two conductors due to the two fields being in the same direction there. Because of the
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
lateral repulsion of the lines of force, the two conductors expensive a mutual force of
repulsion.
F=
µ0 µ r I 1 I 2 l
2 πd
where:
µ 0 - constant permeability, const 33
µ r - relative permeability
l - length in meter (m)
−7
F=
2 x 10 µr I 1 I 2 l
d
I – current in amperes (A)
d – distance between two conductors
SAMPLE PROBLEMS
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
1. A wire 12 cm long and carrying a current of 30A is placed in between the pole face of a
magnet whose magnetic flux density is 0.9 tesla. If the wire is inclined at an angle 60
degrees from the plane of the magnetic field, what is the force exerted on the wire ?
2. Two straight parallel wires 2m long and 3mm apart carries a current of 8A in opposite
direction. Calculate the force between these conductors?
LORENTZ RIGHT HAND RULE

The Lorentz Force Law can be used to describe the effects of a charged particle moving
in a constant magnetic field.

In an open right hand, the direction of the four fingers points to the direction of the
magnetic field, the thumb pointing perpendicular to the four fingers points to the
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
direction of the magnetic force in a positive charge is in the direction in which your open
palm would push.

The implications of this expression include:
1. The force is perpendicular to both the velocity (v) of the charge (q) and the magnetic
field (B)
2. The magnitude of the force F=qvBsinθ where θ is the angle<180 degrees between the
velocity and the magnetic field. This implies that the magnetic force on a stationary
charge or a charge moving parallel to the magnetic field is zero.
3. The direction of the force is given by the right hand rule. The force relationship above is
in the form of a vector product.
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
B – Magnetic field
F – Force
v- velocity/speed
(Wb/ m2 (Tesla)
N
m/s
Max/ cm 2 (Gauss)
Dynes
cm/s
lines/ ¿2
lb f
in/s,ft/s
FLEMING LEFT AND RIGHT HAND RULE

Whenever, a current carrying conductor comes under a magnetic field, there will be force
acting on the conductor and on the other hand, if a conductor is forcefully brought under
a magnetic field, there will be an induced current in that conductor. In both of the
phenomenons, there is a relation between magnetic field, current and force. This relation
is directionally determined by Fleming Left Hand rule and Fleming Right Hand rule
respectively. 'Directionally' means these rules do not show the magnitude but show the
direction of any of the three parameters (magnetic field, current, force) if the direction of
other two are known. Fleming Left Hand rule is mainly applicable for electric motor
and Fleming Right Hand rule is mainly applicable for electric generator. In late 19th
century, John Ambrose Fleming introduced both these rules and as per his name, the rules
are well known as Fleming left and right hand rule.
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
FLEMING LEFT HAND RULE

It is found that whenever a current carrying conductor is placed inside a magnetic field, a
force acts on the conductor, in a direction perpendicular to both the directions of the
current and the magnetic field. In the figure it is shown that, a portion of a conductor of
length L placed vertically in a uniform horizontal magnetic field strength H, produced by
two magnetic poles N and S. If I is the current flowing through this conductor, the
magnitude of the force acts on the conductor is, F = BIL
FLEMING RIGHT HAND RULE
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)

As per Faraday's law of electromagnetic induction, whenever a conductor moves inside a
magnetic field, there will be an induced current in it. If this conductor gets forcefully
moved inside the magnetic field, there will be a relation between the direction of applied
force, magnetic field and the current. This relation among these three directions is
determined by Fleming Right Hand Rule This rule states "Hold out the right hand with
the first finger, second finger and thumb at right angle to each other. If forefinger
represents the direction of the line of force, the thumb points in the direction of motion or
applied force, then second finger points in the direction of the induced current.
SAMPLE PROBLEMS
1. Using the right hand rule, find the direction of the missing information in the diagram
TORQUE ON A FLAT COIL IN A UNIFORM MAGNETIC FIELD
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)

When a current carrying loop is placed across a magnetic field, it has the tendency to be
rotated either clockwise or counter-clockwise dependent on the direction of the magnetic
field and the current. Its direction of rotation is determined using the right hand rule.
Before considering the mathematical nature of the forces on currents in magnetic fields it
is worth just looking at the simple magnetic field diagrams that give rise to these effects.
These are shown in Figure 1. (a) is the field between two magnets, (b) the field due to a
current in a straight wire and (c) the resulting field if they are put together. This last field
is known as the "catapult" field because it tends to catapult the wire out of the field in the
direction shown by the arrow.
T = INAβsinƟ (N-m)
where: N- turns
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
I – current in amperes (A)
A – area of the coil
Ɵ – angle between magnetic field and a perpendicular to the plane
of the coil
SAMPLE PROBLEM:
1. A rectangular loop 10 cm high and 5 cm wide is placed in magnetic field of 0.01
Tesla. If the loop contains turns and carries a current of 50 mA. What is the torque on
it? Assume that the face of the loop is parallel to the field? Given 250 turns.
MAGNETIC CIRCUIT
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)

A closed path in which magnetic induction or flux flows.

A system of magnetic conductors which magnetism maybe established upon the
application of magnetomotive force (mmf)
RELUCTANCE (R)

Property of material that opposes flux flow. It is equal to the ration of the mmf in a
magnetic circuit to the magnetic flux through any cross section of the magnetic circuit.
l
R= µ µ A
o r
units: AT/Wb; Gilbert/Max
Where:
l−¿ Mean length of the magnetic path (m)
µ o - Free space of permeability
µ r−¿ Relative permeability
A – Cross sectional area of the magnetic path (sq. m)
l - mean length / circumference
l−¿ πd ; where d = mean diamete
l−¿ 2πr; where r = radius
Rcgs = 79.577 x 106 Rmks
PERMEANCE (P)

reciprocal of reluctance

Implies the ease or readiness with which magnetic flux is developed.
1
P= R =
µ0 µ r A
l
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
FLUX ( Φ )

Used to indicate the apparent stress in the space surrounding an energized coil or magnet.
Φ=
mmf
R
¿
= R =
0.4 πNI
R
SAMPLE PROBLEMS
1. A certain laminated steel core has a relative permeability of 3000. The length is 5cm and
the cross sectional area is 2sq.m. What is the reluctance?
2 . A magnetic ciruit consists of silicon steel of 3000 permeability of 10 cm length and a
cross section of 1.5 sq. cm and an air gap of the same cross section and of 2 cm length. A
1/2 – ampere current flows through the 50000-turn coil. What is the field intensity at the
air gap ?
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
COMPARISON BETWEEN MAGNETIC AND ELECTRIC CIRCUITS
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
UNITS
SYMBOL
Β
Φ
A
µ0
µr
H
R
MKS
Wb/ m2 (Tesla)
Wb ( Weber)
2
m
Const 33
AT/m
AT/Wb
CGS
Max/ c m2 ( Gauss)
Max (Maxwell)
2
cm
1
Oersted
Gilbert/Max
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
mmf
AT
Gilberts
ENERGY STORED IN A MAGNETIC FIELD
The energy stored in a magnetic field is equal to the work needed to produce

a current through the inductor.
When a conductor carries a current, a magnetic field surrounding the conductor is

produced. The resulting magnetic flux is proportional to the current. If the current
changes, the change in magnetic flux is proportional to the time-rate of change in current
by
a
factor
called
inductance
(L).
Since
nature
abhors
rapid
change,
a voltage (electromotive force, EMF) produced in the conductor opposes the change in
current, which is also proportional to the change in magnetic flux. Thus, inductors oppose
change in current by producing a voltage that ,in turn, creates a current to oppose the
change in magnetic flux; the voltage is proportional to the change in current.
Due to energy conservation, the energy needed to drive the original current must have an

outlet. For an inductor, that outlet is the magnetic field—the energy stored by an inductor
is equal to the work needed to produce a current through the inductor.
W=
1
2
2
R Φ
W=
1
2
2
β
(LA) [
µ
]
W=
1
2
LI2
where:
w – energy stored in Joules (J)
Φ - Flux
µ - permeability of core
β
R – Reluctance
L – Inductance
I – Current
– Magnetic flux density
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
FARADAY’S LAW

A law that states an electrical field is induced in any system in which a magnetic field is
changing with time.

FARADAY’S FIRST LAW OF ELECTROMAGNETIC INDUCTION.


Whenever the flux linking a coil or current changes, an emf is induced in it.
FARADAY’S SECOND LAW OF ELECTROMAGNETIC INDUCTION.

The magnitude of the induced emf is proportional to the rate of change of flux
linkages.
INDUCED EMF – it is the voltage generated by a conductor or coil moving in magnetic field.
e=N
dΦ
dt
where:
e – induced emf (Volt)
N – number of turns
dΦ
dt
- rate of change of flux (Weber per second)
INDUCED EMF

A voltage can be developed in a wire by moving the wire across a magnetic field so that
flux cutting results (Faraday’s Principle)
e = βLv sin Ɵ
where:
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
e – induced emf (volt)
β – flux density at the location of the conductor (Tesla)
L – length of the conductor (meter)
v – relative velocity (meter per second)
e=L
di
dt
where:
e – self- induced emf (volt)
L – self inductance (Henry)
di/dt – rate of change of current ( Ampere per second)
SAMPLE PROBLEMS
1. A coil of 500 turns is linked with a flux of 80,000 maxwells. If the flux is reduced to
zero in 0.01 second, what is the average voltage induced ?
INDUCTANCE

A property of an electric circuit by which emf is induced in it as the result of changing
magnetic flux. it is also a circuit element, typically a conducting coil, in which emf is
generated by electromagnetic induction.
SELF INDUCTANCE
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)

the ratio of emf produced in a circuit by self induction to the rate of change of
current producing it, expressed in Henries (H). Whenever current flows through a
circuit or coil, flux is produced surround it and this flux also links with the coil
itself. It also due to changing current in the coil itself and it is the property of a
coil or solenoid.
L=
NΦ
I
L=
µ0 µ r A N 2
l
L=
N2
R
where:
L – inductance (Henry)
µ 0 - permeability of free space (const 33, 4 π x 10−7 Henry per meter
µ r - relative permeability of the core used
A – cross sectional are of the magnetic path( square meter)
N – number of turns
φ – flux (Weber)
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
I – Current (Ampere)
l - mean length of the magnetic path (meter)
R – reluctance of the magnetic path (AT/Weber)
MUTUAL INDUCTANCE

the ratio of emf in a circuit to the corresponding change of current in a
neighboring circuit. Measures the mutual induction between two magnetically
linked circuits, given as the ratio of the induced emf to the rate of charge of
current producing it, measured in Henries (H)
M=
NΦ
I
M=
SERIES CONNECTED INDUCTORS
µ0 µ r A N 1 N 2
l
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
PARALLEL CONNECTED INDUCTORS
SERIES - PARALLEL CONNECTED INDUCTORS
PARALLEL - SERIES CONNECTED INDUCTORS
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
SERIES COIL WITH MUTUAL INDUCTANCE

Series aiding – sources of electromotive force (emf) which give the ability to the current
to flow in the same direction.
LTA =

L1 +
L2 + 2M
Series opposing – sources of electromotive force (emf) which give the ability to the
current to flow in opposite direction.
L¿ =
L1 +
L2 - 2M
PARALLEL COIL WITH MUTUAL INDUCTANCE

Parallel aiding – this is where connected coils increasing the total equivalent inductance.
2
LTA =

L1 L2−M
L1 + L2−2 M
Parallel opposing – this is where connected coils decreasing the total equivalent
inductance compared to coils that have zero mutual inductance.
LTA =
L1 L2−M 2
L1 + L2 +2 M
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
where:
L1 , L2 - self inductance in H (Henry)
M – Mutual inductance
M=
LTA −LT 0
4
COUPLING FACTOR/ COEFFICIENT OF COUPLING
k=
M
√ L1 L2
SAMPLE PROBLEMS
1.
Two coils in a network are positioned such that there is 80% coupling between them. If
the inductance of one coil is 20mH and the inductance of the other coil is 16mH. Find the
mutual inductance?
2.
A current of 2 Amp through a coil sets up flux linkages of 4Wb-turns. What is the
inductance of the coil?
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
3.
Two coils of inductance
L1
= 1.16 mH,
L2
the total energy stored when the steady current is 2 Amp?
= 2 mH are connected in series. Find
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
EE 419 – BASIC ELECTRICAL ENGINEERING
SEATWORK
Solve the following problems completely. Box your final answer/s. Rounding off should only be
done on your final answers with four decimal places only. Use engineering lettering and avoid
erasures.
1. A flat circular coil with 40 loops of wire has a diameter of 32 cm. What current must flow
in its wires to produce a field of 3.0x 10−4
Wb/ m2 ?
2. A magnetic circuit consists of silicon steel of 3000 relative permeability and air gap. The
length of the steel core is 10cm and the air gap is 2cm. Both have the same cross section
of 1.5 sq.cm. A current of ½ Ampere flows through the windings to produce 2351
Maxwell flux. How many turns are there in the coil?
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
3. A solenoid has 250 turns. What is the magnetomotive force (mmf) in Gilbert when the
current is 0.12 Amp?
4. A coil with 900 turns is wound over a magnetic core with a reluctance of 10000 AT/Wb.
If a current of 2A is passed through the coil, determine the flux density inside the coil?
5. The flux density emanating from a pole of a generator is 20,000 gauss. A conductor one
meter long cuts the flux perpendicularly at the speed of 40 m/sec. What voltage is
developed ?
6. A magnetic coil produces 100,000 maxwells with 2,000 turns and with a current of 2A.
The current is cut-off and the flux collapse in 0.01 sec. What is the average voltage that
will appear across the coil ?
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
7. Find the electromotive force in a conductor of length 50cm moving perpendicular at a
velocity 590m/s to a region of flux density 1 Tesla?
8. The flux density emanating from a pole of a generator is 20,000 Gauss. A conductor one
meter long cuts the flux perpendicularly at a speed of 40m per second. What voltage is
developed?
9.
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
Name: ____________________
SR Code: __________________
__________
Date:______________________
Course & Section:
EE 426- ENERGY CONVERSION
PROBLEM SET NO.1
1.
The force acting on a pole of 3Wb is 12N. The magnetic intensity of the magnetic field is
__.
2.
A wire 12cm long and carrying a current of 30A is placed in between the pole face of a
magnet whose magnetic flux density is 0.9 Tesla. If the wire is inclined at an angle
60degrees from the plane of the magnetic field, what is the force exerted on the wire?
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
3.
The reluctance of a non-magnetic circuit is 12 units. How much flux will be set up if
surrounded by a coil 600 turns carrying a current of 3A.
4.
The relative permeability of a certain silicon steel is 4500. A certain magnetic loop
consists of a silicon steel of 10cm square, 20cm long and an air gap of ¼ cm. What is the
reluctance of the magnetic circuit?
5.
A coil with 900 turns is wound over a magnetic core with a reluctance of 10,000 AT/Wb.
If a current of 0.5A is pass through the coil, how much is the magnetic flux that the coil
generates?
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
6.
A given magnetic circuit has a magnetic field intensity of 400AT/m. If the length of the
magnetic path is doubled maintaining the same magnetomotive force, how much is the
new magnetic field intensity?
7.
A magnetomotive force is supplied by a current of one ampere through 100 turns. The
magnetic circuit consists of a steel core of 1000 permeability, 10cm long and 4 sq. cm.
area and an air gap one cm long. What is the field intensity at the air gap?
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
8.
A non magnetic ring having a cross sectional area of 10 cm 2 is uniformly wound with 300
turns of a given wire. If a current of 1A is passed through the coil, 2.4µWb of flux is
generated inside the ring. Determine the average diameter of the ring.
9.
A coil with 250 turns is wound over a 200cm a cylindrical iron core whose relative
permittivity is 250. If a current of 2A is pass through the coil, determine the flux density
in the core.
10.
A toroidal core with a mean circumference of 100cm and a cross sectional area of 10cm2
is wound with 500 turns of wire. What current would be required to generate a flux of 1
mWb in the core. Assume the core has a relative permeability of 800.
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
11.
A magnetic ring (relative permitivitty=800) has a mean radius of 10cm and a cross
sectional area of 5cm2. An air gap measuring 1.5mm is cut in the ring. Determine the
required mmf in order to produce a flux of 0.25mWb in the air gap.
12.
A magnetic ring with a mean diameter of 25cm and a cross sectional area of 5cm 2 is
wound with a coil of 600 turns. An air gap 4mm is made by cutting a section of the ring.
A current of 10A is passed through the coil. Determine the energy stored in the air gap.
Assume relative permittivity of the ring to be 1000.
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
13.
The energy (Wo) stored in a coil is dependent in the inductance (L) of the coil and the
current flowing. If the inductance were doubled with the same current flowing, what
would be the resulting stored energy?
14.
A 6.0 H coil whose resistance is 12 ohms is connected in series with a 24 ohms resistor
and to a 144 V battery and a switch. The switch is closed at t=0. Determine the energy
stored in the magnetic field at steady state.
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
15.
How much is the inductance of a coil that induces 500V when the current changes at the
rate of 5mA in 2µs?
EE 426-ENERGY CONVERSION
GRADING RUBRIC FOR PROBLEM SET
Name: _________________________________
Instructor Name: Engr. Jonas S. De Castro
Course/Section:_______________
Date:_______________________
Problem Set No: 1
Component
Completeness
Exceptional
All
components are
present and
complete
Correctness
All
components are
completely
correct.
A professional,
polished tone
and format are
maintained
throughout the
Style
Acceptable
All components
are present, but
some are
somewhat
incomplete.
At least one
component
contains a minor
error.
Minor issues of
tone, voice,
spelling,
punctuation, or
formatting.
Marginal
One or more
components are
missing, or all
components are
severely incomplete.
At least one
component contains
a major error.
Major tone or
presentation issues.
DESPONDENT
No genuine attempt
at a complete
solution.
Multiple major
errors, or an
entirely incorrect
response.
Exceedingly terse,
sloppy, or
otherwise
unpolished writing.
GRADE
[Type the document title]
HE called you out of darkness into
HIS wonderful light.
1 Peter 2:9 (NIV)
Clarity
Precision
solution.
All
components are
clear,
organized, and
easy to follow.
No meaningful
ambiguity.
Occasional or
minor issues of
clarity, causing
confusion that
can be overcome
by careful
reading and
charitable
interpretation by
the reader.
Occasional or
minor issues of
precision,
causing
meaningful
ambiguity that
can be overcome
by charitable
interpretation by
the reader.
Truly confusing
writing that can only
be interpreted with
significant effort.
Exceedingly
confusing writing.
Major precision
errors that cause
meaningful
ambiguity in the
interpretation of the
solution, which can
only be resolved
with difficulty (if at
all)
Severely
underspecified
instructions,
definitions, claims,
or arguments