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# Electromagnetism

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• 1. EECE 159 INTRODUCTION TO ELECTROMAGNETISM
• 2.  Magnetic Fd  a. A magnetic fd exists in the region surrounding a permanent magnet/Electromagnet, which can be represented by magnetic flux lines.  b. Magnetic flux lines do not have origins or terminating points in continuous loops.  c. The magnetic flux lines radiate from the north pole to the south pole, returning to the north pole through the bar.  d. The flux lines have equal spacing within the core and symmetric distribution outside the magnetic material.
• 3.  Magnetic Flux(F). The group of magnetic field lines emitted outward from the north pole of a magnet is called magnetic flux. The symbol for magnetic flux is F(phi). The SI unit of magnetic flux is the weber (Wb). One weber is equal to 1 x 108 magnetic field lines.  Example: If a magnetic flux (F) has 5,000 lines, find the number of webers. F 5000 lines 1 x 108 lines/Wb 5 x 103 108 50 x 106 Wb 50 µWb
• 4.  Magnetic Flux Density (B) Magnetic flux density is the amount of magnetic flux per unit area of a section, perpendicular to the direction of flux. The mathematical representation of magnetic flux density is as fol:
• 5.  Magnetomotive Force(Ғ). The flux density of an electromagnet is directly related to the number of turns of, and current through the coil. The product of the two called magnetomotive force, is measured in ampere turns (At).  The magnetomotive force in an inductor is given by: where N is the number of turns of the coil, I is the current in the coil, Φ is the magnetic flux and is the reluctance of the magnetic circuit.
• 6.  Magnetic Permeability( μ). In electromagnetism, permeability is the degree of magnetization of a material that responds linearly to an applied magnetic field. Magnetic permeability is typically represented by the Greek letter μ.  a. Diamagnetic Material. Materials that have permeabilities slightly less than free space (μ0 = 4π×10−7 Wb/A.m.).  b. Paramagnetic Material. Materials that have permeabilities slightly greater than free space(μ0 = 4π×10−7 Wb/A.m.).  c. Ferromagnetic Materials. Materials that have permeabilities thousands time more than free space(μ0 = 4π×10−7 Wb/A.m.). Example- iron, nickel, steel, cobalt and alloys.  d. Relative Permeability. The ratio of permeability of a material to that of the permeability of free space.
• 7.  Magnetic Fd Strength(H). Magnetic fd strength at any point within a magnetic fd is numerically equal to the force experienced by an N-pole of 1 weber placed at that point. Suppose it is required to find the field intensity at a point A distant r meters from a pole of m webers. Than  F=(m1m2)N/(4пμr2) (Newton)  H=(m×1)/(4пμr2) (Newton/Wb)
• 8.  Intensity of Magnetization (I). It may be defined as the induced pole strength developed per unit area of the bar. Also it is the magnetic moment developed per unit volume of the bar. It is the flux density produced in a substance due to its own induced magnetism.  Let m = pole strength induced in the bar in Wb  A = face or pole area of the bar in m3  I =m/A Wb/m2  Or I = M/V (Magnetic moment/volume)
• 9.  Characteristics of Ferromagnetic Material/Theory of ferromagnetism.  a. Ferromagnetic materials exhibit a strong attraction to magnetic fields and are able to retain their magnetic properties after the external field has been removed.  b. Ferromagnetic materials have some unpaired electrons so their atoms have a net magnetic moment.  c. Ferromagnetic materials get their magnetic properties not only because their atoms carry a magnetic moment but also because the material is made up of small regions known as magnetic domains. In each domain, all of the atomic dipoles are coupled together in a preferential direction. This alignment develops as the material develops its crystalline structure during solidification from the molten state.  d. When a ferromagnetic material is in the unmagnitized state, the domains are nearly randomly organized and the net magnetic field for the part as a whole is zero. When a magnetizing force is applied, the domains become aligned to produce a strong magnetic field within the part. Iron, nickel, and cobalt are examples of ferromagnetic materials.
• 10.  B-H Curve.  a. Definition. It may be defined as the lagging of magnetization or induction flux density (B) behind the magnetizing force (H).  b. Basic formula B = μH  c. Steps  (1) No applied field  (2) Saturation  (3) Retentivity  (4) Coercivity  (5) Polarity Reversed  (6) Retentivity  (7) Coercivity  (8) Loop complete.
• 11. Rheostat
• 12. Related Terminologies  Hysteresis  Faraday’s Law Page 472 (Boylestad) N S V N S
• 13.  Lenz’s Law  "An induced current is always in such a direction as to oppose the motion or change causing it"  When an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant. In the examples below, if the B field is increasing, the induced field acts in opposition to it. If it is decreasing, the induced field acts in the direction of the applied field to try to keep it constant.
• 14.  Hysteresis loss  Hysteresis loss is a heat loss caused by the magnetic properties of the armature. When an armature core is in a magnetic field, the magnetic particles of the core tend to line up with the magnetic field. When the armature core is rotating, its magnetic field keeps changing direction. The continuous movement of the magnetic particles, as they try to align themselves with the magnetic field, produces molecular friction. This, in turn, produces heat. This heat is transmitted to the armature windings. The heat causes armature resistances to increase.  To compensate for hysteresis losses, heat-treated silicon steel laminations are used in most dc generator armatures. After the steel has been formed to the proper shape, the laminations are heated and allowed to cool. This annealing process reduces the hysteresis loss to a low value.
• 15.  Eddy Current  An eddy current (also known as Foucault current) is an electrical phenomenon discovered by French physicist Léon Foucault in 1851. It is caused when a conductor is exposed to a changing magnetic field due to relative motion of the field source and conductor; or due to variations of the field with time. This can cause a circulating flow of electrons, or a current, within the body of the conductor. These circulating eddies of current create induced magnetic fields that oppose the change of the original magnetic field due to Lenz's law, causing repulsive or drag forces between the conductor and the magnet. The stronger the applied magnetic field, or the greater the electrical conductivity of the conductor, or the faster the field that the conductor is exposed to changes, then the greater the currents that are developed and the greater the opposing field.
• 16.  Eddy Current loss  The core of a generator armature is made from soft iron, which is a conducting material with desirable magnetic characteristics. Any conductor will have currents induced in it when it is rotated in a magnetic field. These currents that are induced in the generator armature core are called EDDY CURRENTS. The power dissipated in the form of heat, as a result of the eddy currents, is considered a loss.  (7)Core loss  Core loss (or iron loss) is a form of energy loss that occurs in electrical transformers and other inductors. The loss is due to a variety of mechanisms related to the fluctuating magnetic field, such as eddy currents and hysteresis. Most of the energy is released as heat, although some may appear as sound ("hum"). Core losses do not include the losses due to resistance in the conductors of the windings, which is often termed "copper loss".