Magnet
A magnet is a material (substance) that attracts a
magnetic material. The relationship between magnetism and electricity has led
to the invention of appliances such as radio set, television set, loud
speakers, transformers, electric motors, microphone, etc.
Magnetic Circuit
It is an interconnected set of magnetic material in which magnetic flux is established.
Solenoid: It is a coil
with multiple numbers of coils.
Electromagnet: It is a coil
whose core is an iron.
Exaltation
Current: It is the current in a coil.
What is magnetic field and unit?
Magnetic Field
It is the region around a magnet where the effect of magnetic field can be detected.
Magnetic Flux (Ф)
It is the amount of magnetic field produced by a magnetic source. The unit is the Weber (Wb).
Magnetic Flux Density (B)
It is the amount of flux passing through an area which is perpendicular to the direction of the flux. The SI unit is Tesla (T).
Magnetic flux density formula
Magnetic field formula
Magneto motive Force (F)
Magnetic Field Strength (H)
It is the mmf per unit length of the magnetic circuit. It is called magnetizing force or magnetic field intensity.
Relative Permeability (μr)
It is defined as the ratio of flux density in a material to the flux density in a vacuum.
Relative permeability μr varies the type of material since is a ratio of densities. It has no unit. In vacuum μr = 1
B = μoμr OR 𝜇𝑟 = 𝐵
H 𝜇𝑜H
Permeability of Free Space (μo)
It is the ratio of the magnetic flux density to the magnetic field strength. It is constant
μo = 𝟒𝝅 × 𝟏𝟎−𝟕𝑯/𝒎
B = μo
H
Reluctance (S)
It is the magnetic equivalent of resistance in the electrical circuit.
𝑆 = 𝑙 , A/Wb
𝜇𝑜𝜇𝑟𝐴
F = ФS (Ohm’s law for magnetic circuit)
The unit of reluctance is A/Wb
Magnetic field strength formula example
1) An iron ring of mean circumference 100cm and of uniform cross –sectional area 5cm2 has a coil consisting of 500 turns. The current through the coil is 5A and the relative permeability of iron is 450.
Calculate
(a) The magnetizing force
(b) The flux density
(c) The total flux
Solution
Length (L) = 100cm = 100 x 10-2 = 100 = 1m
100
Area (A) = 5𝑐𝑚2 = 5 x
(10−2)2 = 5 x
10−4 = 0.0005𝑚
Turns (N) = 500
Current (I) = 5A
Relative Permeability (μr) = 450
Magnetizing force (H) =?
Flux density (B) =?
Total flux (∅) =?
(a) Magnetizing force (H)
H = N1 = 500 x 5
= 2500
L 100 x 10-2 1
= 2500A/M
(b) The flux density
B = μoμr
H
B = μoμr H
= 4π x 10-7 x 450 x 2500
= 1.414T
(c)Total Flux (∅)
B = (∅)
𝐴
∅ = BA
∅ = 1.414 × 5 × 10−4
= 0.00707wb
= 707μwb
2) A magnetic circuit has a cross – sectional area of 6 x 10-4m2 and mean length of 0.3m. A 40 – turn coil is rounded uniformly round the core. When a current of 1.5A passes in the coil, flux density of 0.5T was established in the circuit.
Calculate;
(a) The magnetic field strength
(b) The relative permeability of the magnetic material
Solution
Area (A) = 6 x 104m2
= 60000m2
Length (L) = 0.3m
Turn (N) = 40
Current (I) = 1.5A
Flux density (B) = 0.5T
Magnetic field strength (H) =?
Relative permeability (μr) =?
(a) Magnetic field strength (H)
H = N1 = 40 x 1.5 = 200A/M
L 0.3
b. Relative permeability (μr)
B = μoμr
H
B = μoμr H
μr = B = 0. 5 = 0.
5 =
μoH 4π x 10-7 x
200 0.00025736
= 1989.43
3) A coil is wound on wooden ring of rectangular section with an axial length of 2cm and radial thickness 2cm. if the mean diameter of the coil is 15cm, calculate the reluctance of the magnetic circuit. If the wooden ring is replaced by an iron of the same shape whose relative permeability is 1000, calculate the reluctance of the iron ring.
Solution
Axial length (L) = 2cm
Radial thickness (b) = 2cm
Area (A) = 2 × 10−2 × 2 × 10−2 = 4 × 10−4𝑚2
Length (L) = 𝜋𝑙 𝑙 = 15 × 10−2 = 0.471𝑚
Relative permeability (μr) = 1000
(a). Reluctance of wooden ring.
S = 𝑙 = 0.471
μoA 4𝜋 x 10-7 x 4 x 10-4
= 0.937 x 109A/wb
=
937000000 𝐴/𝑤𝑏
(b) Reluctance of iron ring
S = 𝑙 = 0.471
μoμrA 4𝜋 x 10-7 x 1000 x 4 x 10-4
Magnetization Curve of Ferromagnetic Materials
In an air – care coil, increasing the magnetizing force has the effect causing the flux density in the core to increase linearly form zero.
Magnetizing curve
When a ferromagnetic core is inserted in to the coil, a magnetizing curve (OA) is formed. Magnetic domains is the spinning motion of electrons in ferromagnetic material that produces tiny permanent magnetic effect between points 0 and k the flux density increases very rapidly because the application of a magnet field to the material causes the magnetic domains to align with the magnetic fluid. When the values of magnetizing force exceed. Hk, the rate increases of flux density diminishes because loss magnetic domains remain to be lined up.
Beyond the point marked, the curve is parallel to the line for the air – core coil because all the magnetic domains point in the direction of the applied field.
A material is said to be magnetically saturated when all the magnetic domain point in the directions of the applied field.
HYSTERESIS LOOP
Hysteresis loop is a graphical representation use to describe how flux density varies with magnetic field strength in ferromagnetic material.
To plot a complete curve of how B varies with H, it is necessary to demagnetize the ferromagnetic material in a closed ring.
Demagnetization is achieved by gradually reducing the current through the magnetizing coil from a high value to zero and reversing the direction of the current repeatedly. E.g. of picture tube of a color TV set demagnetized when switched on. When the magnetizing force is reduced to zero, not all of the magnet domains material retains some magnetism called Remnant flux density.
Remanent Flux Density (Br)
It is the flux density remaining in the iron when reducing the magnetizing force to zero.
If the magnetizing force is increased in the reverse direction, the flux density gradually reduces to zero.
Coersive Fore (Hc)
It is a reversed magnetizing force used to reduce (wipe out) the residual (remanent) flux density.
Trial Test
A magnetize circuit consist of three parts X, Y and Z in series each with a uniform cross – section area.
Part length (cm) Area (cm2)
X 35 4.5
Y 10 3.0
Z 0.1 3.5
Part Z in air gap. Neglecting magnetic leakage and fringing, determine the number of ampere turn necessary on a coil which is uniformly wound on the magnetic circuit and produces a flux of 0.35mWb in the air gap, if the magnetic field strength of X is 490A/M and Y in 1360A/M Solution
Part X
= 0.778T
mmf (F) = HL
= 490 x 35 x 10-2
= 171.5At
Part Y
B
= 1.167T
mmf(F) = HL
= 1360 x 10 x 10-2
= 136AT
F = 136AT
Part Z
Reluctance s
S = 𝑙 = 0.1 x 10-2
μoA 4𝜋 x 10-7 x 3.5 x 10-4
= 2.274 x 106A/wb
S = 2274000A /wb
Mmf (F) = ᶲS
= 0.35x10-3 x 2274000
= 795.9
= 796At
Total mmf requirement = Fx + Fy +
Fz
=
171.5 + 136 + 796
=
1103.5At
COMPARISON BETWEEN DC ELECTRIC CIRCUIT AND MAGNETIC CIRCUIT
|
ELECTRIC CIRCUIT |
UNIT |
MAGNETIC CIRCUIT |
UNIT |
|
Ohm’s law: V = IR |
Volt |
Ohm’s law: F = ФS |
Ampere-turn |
|
Electromotive Force (Emf) |
Volt |
Magnetomotive Force (mmf) |
Ampere-turn |
|
Electric Current (I) |
Ampere |
Magnetic Flux (Ф) |
Weber |
|
Resistance R = l/𝝳A |
Ohm’s |
Reluctance S = l/μA |
Ampere-turn |
|
Conductivity 𝝳 |
Siemens |
Permeability μ |
Henry/metre |
|
Electric Field Strength E |
Volt/metre |
Magnetic Field Strength H |
Ampere-turn |
|
Current Density
|
A/m2 |
Magnetic Flux Density B |
Tesla |
Trial Test
(1) A coil of 500 turns is wounded on an iron ring. The ring has a mean cross – sectional area of 5cm2. If the total flux in the ring is 1.5 × 10−3wb and the relative permeability of the ring is 45.
Calculate;
(a) The flux density
(b) The magnetizing
(c)The reluctance of the circuit
(2) A mild steel ring has a mean circumference of 500mm and a uniform cross-sectional area of 300mm2. Calculate the mmf required to produce a flux of 500μWb.
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