Manuel, Michael Brian D.BSEE IV -3 DC Machine ( ELEN 3444)Prof. Engr. Vilma Perez

1) State the law of electrostatic explains and give example. COULOMB’S LAW (LAW OF ELECTRIC FORCE)First law of electric force:Like charges repel each other and unlike charges attract each other.Second law of electric force:The force of attraction or repulsion between charges is directly proportional to the product of two charges and inversely proportional to the square of the distance between them.

Where: F = force (SI units: Newton and CGS units: Dynes) Q1 &Q2 = Charge In each body (SI unit: Coulomb and CGS unit: Statcoulomb) 1 Coulomb = 3 x 109 Statcoulomb ∑o =absolute permittivity = 8.854 x 10−12 farad per meter ∑r = relative permittivity or dielectric constant = 1, for free space d = r = distance between the two bodies (SI unit: meter and CGS unit: centimeter) k = constant in SI units equal to 9 x 109

2) Define the following:What is electrostatic induction?Modification in the distribution of electric charge on one material under the influence of nearby objects that have electric charge. Thus, because of the electric force between charged particles that constitute materials, a negatively charged object brought near an electrically neutral object induces a positive charge on the near side and a negative charge on the far side of the neutral object. The neutral object, furthermore, may sometimes become charged positively by induction, if its negative part is grounded momentarily to permit the negative charge to escape. Electrostatic induction occurs whenever any object is placed in an electric field.

What is electric field intensity?The force per unit charge that will act at a point in the field on a very small test charge placed at that location.Electric field intensity exerts an electric force on any other charged object within the field.

Where: E = electric intensity (newton per coulomb) d = distance in meters of the test charge (1C) to the charge (Q) body

Field intensity outside an isolated sphere in free spaceIt is the field intensity of a summation of charge that creates a sphere like figure.

Where: E = electric field intensity (volt per meter) at a distance r (meter) from the center of an isolated charged sphere located in free space. Q = total charge (coulomb) which is distributed uniformly on the sphere.Electric field intensity created by an isolated, charge long cylindrical wire in free space- It is the field intensity of a summation of charge that creates a cylindrical like figure.

Where: E = electric field (volt per meter) = charge per unit of length (coulomb per meter) distributed uniformly over the surface of Δthe isolated cylinder. r = distance in meter from the center of the cylinder to the point at which the electric field intensity is evaluated.

What is potential and potential difference?Potential difference defined as the work done in transferring a unit positive charge from one point to other.A positive charge q in an electric field of intensity E experience a force, when q is moved from one point A to another B in the field work is done. If this field work done it is divided by the charge, the result is the potential difference A and B.

What is potential at a point due to a chargePotential at point can be defined if some arbitrary point is taken as a reference having zero or definite potential.

3) State the laws of magnetic force. Define pole strength, permeability, absolute permeability, magnetic potential, magnetizing force, flux density.LAW OF MAGNETIC FORCE

- The magnetic field B is defined from the Lorentz Force Law, and specifically from the magnetic force on a moving charge:

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 is F = qvB sin where is the angle < 180 degrees between the θ θvelocity 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.

When the magnetic force relationship is applied to a current-carrying wire, the right-hand rule may be used to determine the direction of force on the wire.From the force relationship above it can be deduced that the units of magnetic field are Newton seconds /(Coulomb meter) or Newtons per Ampere meter. This unit is named the Tesla. It is a large unit, and the smaller unit Gauss is used for small fields like the Earth's magnetic field. A Tesla is 10,000 Gauss. The Earth's magnetic field at the surface is on the order of half a Gauss.

POLE STRENGHT- A quantity that corresponds to the amount of magnetic flux emanating from a given magnetic

pole and expressed in terms of the unit magnetic pole.

\PERMEABILITY

- It is the measure of the ability of a material to support the formation of a magnetic field within itself. Hence, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically represented by the Greek letter µ.

- The ability of a material to conduct a magnetic flux through it.

Where: µ = permeability of material (henry per meter) = magnetic flux density (tesla)β

H = magnetic flux intensity (ampere turn per meter)

ABSOLUTE PERMEABILITY- It is the ratio of the magnetic flux density to the intensity of the magnetic field in a medium.

The measurement is in webers per square meter in the meter-kilogram-second system. It is also known as induced capacity.

MAGNETIC POTENTIAL- A magnetic dipole moment in a magnetic field will possess potential energywhich depends

upon its orientation with respect to the magnetic field. Since magnetic sources are inherently dipole sources which can be visualized as a current loop with current I and area A, the energy is usually expressed in terms of the magnetic dipole moment:

The energy is expressed as a scalar product, and implies that the energy is lowest when the magnetic moment is aligned with the magnetic field. The difference in energy between aligned and anti-aligned is

The expression for magnetic potential energy can be developed from the expression for the magnetic torque on a current loop.

MAGNETIC POTENTIAL- It is the part of the magnetic induction that is determined at any point in space by the

current density and displacement current at any point independently of the magnetic or other physical properties of the surrounding medium.

FLUX DENSITY- It is a measure or rate of flow of a fluid, particles or energy per unit area.

where

4) What is electromagnetism, force on the current carrying conductor in the magnetic field, magnetizing force of a long straight conductor, magnetizing force of a long solenoid, force between two parallel conductors.

4.1 Electromagnetism-In the relationship between electricity and magnetism, magnetic flux exists in circles around the conductor (where there is no other magnetic field in the vicinity).These circles have their centers at the axis of the conductor, and their planes are perpendicular to the conductor. The direction of this magnetic field depends on the direction of the current. If a cylindrical conductor carrying current is brought vertically downwards through the sheet of cardboard, iron filings sprinkled on the cardboard from circles from circles concentric with the conductor. There are two simple rules by which the relationship between direction of the current in a conductor and the direction of the magnetic field surrounding the conductor are determined:

4.1.1 Hand Rule-Grasp the conductor in the right hand with the thumb pointing in the direction of the current.

The fingers will then point in the direction of the lines in flux.4.1.2 Corkscrew Rule-The direction of the current and that of the resulting magnetic field are related to each other as

the forward travel of a corkscrew and the direction in which it rotated.

4.2 Force on the current carrying conductor in magnetic field.-Conductor carrying currents in the same directions tend to be drawn together; conductors carrying currents in opposite directions tend to be repelled from one another. All electric circuits tend to take such a position as will make their currents parallel and flowing in the same direction.

Where: F = force (newton) = flux density (tesla) I = current (ampere) L = length of conductor (meter)

4.3 Magnetizing force of a long straight conductor-Current running through a wire will produce both an electric field and magnetic field. For a closed curve and magnetic field related to current as in Ampere’s law. This can be related to the Biot-Savart law. For a straight length of conductor this law generally generates partial magnetic field as a function of current for a segment of wire at a point distance away from the conductor.

F=(2x 10−7)( I )(I ) Ld

Where: d = distance between the two wire (meter)

4.4 Magnetizing force of a long solenoid- A solenoid is a coil of wire designed to create a strong magnetic field inside the coil. By wrapping the same wire many times around a cylinder, the magnetic field due to the wires can become quite strong. The number of turns refers to the number of loops the solenoid has. More loops will bring about a

stronger magnetic field. Ampere's law can be applied to find the magnetic field inside of a long solenoid as a function of the number of turns per length and the current. The magnetic field inside a solenoid is proportional to both the applied current and the number of turns per unit length. There’s no dependence on the diameter of the solenoid or even on the fact that the wires were wrapped around a cylinder and not a rectangular shape. The magnetic field is constant inside the solenoid.

F= ¿L

Where: N = no. of turns of solenoidI = current carrying on solenoid (ampere)

4.5 Force between two parallel conductors- Parallel wires carrying current produce significant magnetic fields, which in turn produce significant forces on currents. The force felt between the wires is used to define the standard unit of current, known as an ampere. If the currents are in the same direction, the force attracts the wires. If the currents are in opposite directions, the force repels the wires.

F=2KI I Lr

Where: F = force (newton)K = 10−7w/amp-mI & I = current carrying of the two conductorR = distance between the two conductor

5.) Define the following: Magnetic Circuit, Magnetomotive Force, Reluctance, Permeance, Reluctivity, Dynamically Induced Emf, Statically Induced Emf and Self Induced Emf.

Magnetic circuit, closed path to which a magnetic field, represented as lines of magnetic flux, is confined. In contrast to an electric circuit through which electric charge flows, nothing actually flows in a magnetic circuit.

In a ring-shaped electromagnet with a small air gap, the magnetic field or flux is almost entirely confined to the metal core and the air gap, which together form the magnetic circuit. In an electric motor, the magnetic field is largely confined to the magnetic pole pieces, the rotor, the air gaps between the rotor and the pole pieces, and the metal frame. Each magnetic field line makes a complete unbroken loop. All the lines together constitute the total flux. If the flux is divided, so that part of it is confined to a portion of the device and part to another, the magnetic circuit is called parallel. If all the flux is confined to a single closed loop, as in a ring-shaped electromagnet, the circuit is called a series magnetic circuit.

In analogy to an electric circuit in which the current, the electromotive force(voltage), and the resistance are related by Ohm’s law (current equals electromotive force divided by resistance), a similar relation has been developed to describe a magnetic circuit.

The magnetic flux is analogous to the electric current. The magnetomotive force, mmf, is analogous to the electromotive force and may be considered the factor that sets up the flux. The mmf is equivalent to a number of turns of wire carrying an electric current and has units of ampere-turns. If either the current through a coil (as in an electromagnet) or the number of turns of wire in the coil is increased, the mmf is greater; and if the rest of the magnetic circuit remains the same, the magnetic flux increases proportionally.

The reluctance of a magnetic circuit is analogous to the resistance of an electric circuit. Reluctance depends on the geometrical and material properties of the circuit that offer opposition to the presence of magnetic flux. Reluctance of a given part of a magnetic circuit is proportional to its length and inversely proportional to its cross-sectional area and a magnetic property of the given material called its permeability. Iron, for example, has an extremely high permeability as compared to air so that it has a comparatively small reluctance, or it offers relatively little opposition to the presence of magnetic flux. In a series magnetic circuit, the total reluctance equals the sum of the individual reluctances encountered around the closed flux path. In a magnetic circuit, in summary, the magnetic flux is quantitatively equal to the magnetomotive force divided by the reluctance.

Permeance, in general, is the degree to which a material admits a flow of matter or energy.

Permeance is the inverse of reluctance. Permeance is a measure of the quantity of flux for a number of current-turns in magnetic circuit. A magnetic circuit almost acts as though the flux is 'conducted', therefore permeance is larger for large cross sections of a material and smaller for longer lengths. This concept is analogous to electrical conductance in the electric circuit.

Magnetic permeance is defined as the reciprocal of magnetic reluctance

Reluctivity is the tendency of a magnetic circuit to conduct magnetic flux, equal to the reciprocal of the permeability of the circuit.

When a flux linking a coil or conductor changes, an EMF is induced to it.

Methods of Inducing EMF in a conductor

1. Dynamically Induced EMF

2. Statically Induced EMF

-Self Induced EMF

If the conductor is moved in a stationary magnetic field in such a way that the flux linkages with it changes, then it’s Dynamically Induced EMF.

Statically Induced EMF – The EMF is induced in the conductor when the conductor is in stationary and the field is changing.

Self-Induced EMF – It is the EMF which is induced in the conductor by changing in its own. When current is changing the magnetic field is also changing around the coil and hence Faraday law is applied here and EMF are induced in the coil to itself. Any electrical circuit in which the change of current is accompanied by the change of flux and thereby induced EMF is said to be inductive or to possess self-inductance.