Whenever movement of electrons is produced by a
directive force (i.e. a potential difference), a magnetic field is always
associated with that movement. The magnitude and direction of this field
depends on the rate of flow of the electrons i.e. the current (IA = 6.2 x 1018
electrons/second) and the direction of such a flow. The shape of the field
depends on the path taken by the electrons. In general, if the electrons travel
in a linear path, the magnetic field will be circular in cross-section and if
the electrons travel in a circular path will be linear.
directive force (i.e. a potential difference), a magnetic field is always
associated with that movement. The magnitude and direction of this field
depends on the rate of flow of the electrons i.e. the current (IA = 6.2 x 1018
electrons/second) and the direction of such a flow. The shape of the field
depends on the path taken by the electrons. In general, if the electrons travel
in a linear path, the magnetic field will be circular in cross-section and if
the electrons travel in a circular path will be linear.
Magnetic field due to Electrons moving in a
straight line
straight line
Where
µ0 is the permeability of free space and is a constant which equals
to 0.4π x 10-6 or 1.257 x 10-6 SI units. The flux density
is equal to the total flux (Ф) in Weber (Wb) divided by the area (A) of the
field in square metres (m2)
µ0 is the permeability of free space and is a constant which equals
to 0.4π x 10-6 or 1.257 x 10-6 SI units. The flux density
is equal to the total flux (Ф) in Weber (Wb) divided by the area (A) of the
field in square metres (m2)
B = Ф/A
Hence 1 Tesla (T) =
1wb/m2
1wb/m2
Magnetic lines of
force around a solenoid
force around a solenoid
Figurative
speaking, for a straight conductor, right hand rule states that when you grasp
the conductor with the right hand so that the thumb point in the direction of
conventional current, the finger circling the conductor then point in the
direction of the magnetic lines of force around the conductor.
speaking, for a straight conductor, right hand rule states that when you grasp
the conductor with the right hand so that the thumb point in the direction of
conventional current, the finger circling the conductor then point in the
direction of the magnetic lines of force around the conductor.
The
magnetic field of a conductor can further be concentrated by winding a
conductor around a cardboard tube as shown in figure 1 above to form a
solenoid. Because the current in the adjacent turns of the solenoid is in the
same direction around the circumference of the coil, the solenoid behaves as a
single loop of a stranded conductor, each strand carrying a current equal to
the actual solenoid current. This will result in a magnetic field around the
solenoid having the pattern shown in figure 1 above. Since this magnetic field
pattern is similar to that of a bar magnet, we can meaningfully say that we
have produced an electromagnet.
magnetic field of a conductor can further be concentrated by winding a
conductor around a cardboard tube as shown in figure 1 above to form a
solenoid. Because the current in the adjacent turns of the solenoid is in the
same direction around the circumference of the coil, the solenoid behaves as a
single loop of a stranded conductor, each strand carrying a current equal to
the actual solenoid current. This will result in a magnetic field around the
solenoid having the pattern shown in figure 1 above. Since this magnetic field
pattern is similar to that of a bar magnet, we can meaningfully say that we
have produced an electromagnet.
Applying
the right hand rule for direction of magnetic lines of force around a straight
conductor to a solenoid, we obtain:
the right hand rule for direction of magnetic lines of force around a straight
conductor to a solenoid, we obtain:
Grasp
the solenoid with the right hand so that the fingers follow the conventional
current direction around the circumference of the solenoid, the thumb then
points in the direction of the magnetic lines of force through the centre of
the solenoid
the solenoid with the right hand so that the fingers follow the conventional
current direction around the circumference of the solenoid, the thumb then
points in the direction of the magnetic lines of force through the centre of
the solenoid
Force
Acting on Electros Moving Perpendicularly to a Magnetic Field
Acting on Electros Moving Perpendicularly to a Magnetic Field
When
electrons move at right angles to a constant magnetic field, the magnetic field
produced by the moment of the electrons distorts the main field which is in a
state of tension. Consequently the main field, in trying to return to a state
of stability, will exert a force on the electrons. If the electron path is
through a conductor then this force will be transferred to the conductor. The
force will act in a direction perpendicular to both the direction of electron flow
and the magnetic field. The magnitude of the force varies directly with the
flux density (B) of the field, the rate of flow of the electrons i.e. the
current (I) and the length of the electron path of the field (L).
electrons move at right angles to a constant magnetic field, the magnetic field
produced by the moment of the electrons distorts the main field which is in a
state of tension. Consequently the main field, in trying to return to a state
of stability, will exert a force on the electrons. If the electron path is
through a conductor then this force will be transferred to the conductor. The
force will act in a direction perpendicular to both the direction of electron flow
and the magnetic field. The magnitude of the force varies directly with the
flux density (B) of the field, the rate of flow of the electrons i.e. the
current (I) and the length of the electron path of the field (L).
If
these quantities are measured in their fundamental units, Tesla, ampere and
metre then
these quantities are measured in their fundamental units, Tesla, ampere and
metre then
F =
BIL (in Newton)
BIL (in Newton)
Magneto
motive Force
motive Force
Just
as an electric current cannot flow in an electric circuit until we connect it
to a voltage source, magnetic flux (magnetic line of force) cannot be
established until a magneto motive force is produced.
as an electric current cannot flow in an electric circuit until we connect it
to a voltage source, magnetic flux (magnetic line of force) cannot be
established until a magneto motive force is produced.
Magneto
motive force in a magnetic circuit is the counterpart of electromotive force in
an electric circuit.
motive force in a magnetic circuit is the counterpart of electromotive force in
an electric circuit.
In
an electromagnet, magnetic flux appears only when electric current flows in a
solenoid. Therefore, magneto motive force (mmf) must be a direct result of
electric current. We can therefore establish a unit of mmf on the basis of the
electric current in a single turn coil of a wire
an electromagnet, magnetic flux appears only when electric current flows in a
solenoid. Therefore, magneto motive force (mmf) must be a direct result of
electric current. We can therefore establish a unit of mmf on the basis of the
electric current in a single turn coil of a wire
Hence,
the ampere is the SI unit of magneto motive force. Since adding turns of wire
to a solenoid produces the same effect as adding an extra strand to a single
turn coil, each strand carrying the input current tot he coil, the effective amperes of magneto
motive force is the product of the coil current and the number of turn in the
coil.
the ampere is the SI unit of magneto motive force. Since adding turns of wire
to a solenoid produces the same effect as adding an extra strand to a single
turn coil, each strand carrying the input current tot he coil, the effective amperes of magneto
motive force is the product of the coil current and the number of turn in the
coil.
The
letter symbol for magneto motive force is Fm
letter symbol for magneto motive force is Fm
Fm
= NI
= NI
Where
N is the number of turns in the coil, I is the actual current flowing through
the coil and Fm is the magneto motive force in ampere (effective).
N is the number of turns in the coil, I is the actual current flowing through
the coil and Fm is the magneto motive force in ampere (effective).
So
that e do not forget that the total magneto motive force is the product of
actual coil current and the number of turns of wire in the coil, we can say
that the ampere turn is the practical unit of magneto motive force
that e do not forget that the total magneto motive force is the product of
actual coil current and the number of turns of wire in the coil, we can say
that the ampere turn is the practical unit of magneto motive force
Some
basic calculations on Electromagnetism
basic calculations on Electromagnetism
Example
1
1
A conductor of length 200mm is placed at right
angles to a magnetic field of density 0.2T. If a current of 10A is maintained
in the conductor, calculate the force which acts on the conductor.
angles to a magnetic field of density 0.2T. If a current of 10A is maintained
in the conductor, calculate the force which acts on the conductor.
Solution
Length
(L) = 200mm = 200 x 10-3m
(L) = 200mm = 200 x 10-3m
Magnetic
flux density (B) = 0.2 T
flux density (B) = 0.2 T
Current
(I) = 10A
(I) = 10A
Force
= BIL
= BIL
= 0.2 x 10 x 200 x 10-3
= 0.4N
Example
2
2
An
air closed coil wound with 500 turns, has a length of 250mm and a cross
sectional area of 400mm2. Calculate the magneto motive force, the
magnetising force (H) and the total flux produced when a current of 5A is
maintained in the coil
air closed coil wound with 500 turns, has a length of 250mm and a cross
sectional area of 400mm2. Calculate the magneto motive force, the
magnetising force (H) and the total flux produced when a current of 5A is
maintained in the coil
Solution
Length
(L) = 250mm = 250 x 10-3
(L) = 250mm = 250 x 10-3
Number
of turns (N) = 500 turns
of turns (N) = 500 turns
Cross
sectional area (A) = 400mm2 = 400 x 10-6
sectional area (A) = 400mm2 = 400 x 10-6
Current
(I) = 5A
(I) = 5A
Magneto
motive force (Fm) = NI
motive force (Fm) = NI
=
500 x 5
500 x 5
=
2500A-turns
2500A-turns
Magnetising
force (H) = Fm (magneto
motive force per unit length)
force (H) = Fm (magneto
motive force per unit length)
L
=2500
250 x 10-3
= 1 x 104
A-T/M
A-T/M
= 10 K
A/M
A/M
Total
Flux (Ф) = BA
Flux (Ф) = BA
Where B = μoH
Ф= μoHA
= 0.4π x
10-6 x 104 x 400 x 10-6Wb
10-6 x 104 x 400 x 10-6Wb
= 5.03 x 10-6Wb
= 5.03μWb
Example
3
3
A
coil of 200 turns is wound on an iron core of length 250mm and a cross
sectional area of 400mm2. If the iron has a relative permeability of
800, estimate the total flux produced when a current of 1.5A is maintained in
the coil
coil of 200 turns is wound on an iron core of length 250mm and a cross
sectional area of 400mm2. If the iron has a relative permeability of
800, estimate the total flux produced when a current of 1.5A is maintained in
the coil
Solution
Number
of turns (N) = 200 turns
of turns (N) = 200 turns
Length
(L) = 250mm = 250 x 103m
(L) = 250mm = 250 x 103m
Cross
sectional Area (A) = 400mm2= 400 x 10-6m2
sectional Area (A) = 400mm2= 400 x 10-6m2
Relative
Permeability (μr) = 800
Permeability (μr) = 800
Current
(I) = 1.5 A
(I) = 1.5 A
Total
flux (Ф) = BA
flux (Ф) = BA
But
B = μoμrh
B = μoμrh
And H = Fm
L
Fm
= NI
= NI
Therefore,
Ф = μoμrNIA
Ф = μoμrNIA
L
