LORENTZ FORCE LAW BASIC DEFINITION AND TUTORIALS

The Lorentz Force Law


F = q(E + v × B) (3.1), gives the force F on a particle of charge q in the presence of electric and magnetic fields. In SI units, F is in newtons, q in coulombs, E in volts per meter, B in teslas, and v, which is the velocity of the particle relative to the magnetic field, in meters per second.

Thus, in a pure electric-field system, the force is determined simply by the charge on the particle and the electric field

F = qE (1)

The force acts in the direction of the electric field and is independent of any particle motion. In pure magnetic-field systems, the situation is somewhat more complex. Here the force

F = q(v × B) (2)

is determined by the magnitude of the charge on the particle and the magnitude of the B field as well as the velocity of the particle. In fact, the direction of the force is always perpendicular to the direction of both the particle motion and that of the magnetic field. Mathematically, this is indicated by the vector cross product v× B in Eq. 2.

The magnitude of this cross product is equal to the product of the magnitudes of v and B and the sine of the angle between them; its direction can be found from the right-hand rule, which states that when the thumb of the fight hand points in the direction of v and the index finger points in the direction of B, the force, which is perpendicular to the directions of both B and v, points in the direction normal to the palm of the hand, as shown in Fig below.

For situations where large numbers of charged particles are in motion, it is convenient to rewrite Eq. 1 in terms of the charge density p (measured in units of coulombs per cubic meter) as

Fv = p(E + v × B) (3)

where the subscript v indicates that Fv is a force density (force per unit volume) which in SI units is measured in newtons per cubic meter. The product p v is known as the current density

J = pv

which has the units of amperes per square meter. The magnetic-system force density corresponding to Eq. 3 can then be written as

Fv = J x B (3.6)

For currents flowing in conducting media, Eq. 3.6 can be used to find the force density acting on the material itself. Note that a considerable amount of physics is hidden in this seemingly simple statement, since the mechanism by which the force is transferred from the moving charges to the conducting medium is a complex one.

SHUNT WOUND GENERATOR BASIC AND TUTORIALS

WHAT ARE SHUNT WOUND GENERATORS?


The shunt-wound generator is shown diagrammatically in Figure below. A small part of the total current, the exciting current, is shunted through the fields. The exciting current varies from possibly 5 percent of the total current in small machines to 1 percent in large ones.

The exciting current is determined by the voltage at the brushes and the resistance of the field winding. Residual magnetism in the field cores permits a shunt generator to “build-up.” This small amount of magnetism that is retained in the field cores induces a voltage in the armature (William H. Timbie, Elements of Electricity).

This voltage sends a slight current through the field coils, which increases the magnetization. Thus, the induced voltage in the armature is increased. This in turn increases the current in the fields, which still further increases the magnetization, and so on, until the normal voltage of the machine is reached and conditions are stable. This “building-up” action is the same for any self-excited generator and often requires 20 to 30 s.

If a shunt generator (Timbie) runs at a constant speed, as more and more current is drawn from the generator, the voltage across the brushes fails slightly. This fall is due to the act that more and more of the generated voltage is required to force the increasing current through the windings of the armature; i.e., the armature IR drop increases.

This leaves a smaller part of the total emf for brush emf, and when the brush voltage falls, there is a slight decrease in the field current, which is determined by the brush voltage. This and armature reactions cause the total emf to drop a little, which still further lowers the brush potential. These causes combine to lower the voltage gradually, especially at heavy overloads.

The curve in Fig.III, shows these characteristics. For small loads the curves is nearly horizontal, but at heavy overloads it shows a decided drop. The point at which the voltage of a commercial machine drops off rapidly is beyond the operating range and is of importance only for short-circuit conditions.

The voltage of a shunt machine can be kept fairly constant by providing extra resistance in the field circuit, which may be cut out as the brush potential falls.

This will allow more current to flow through the field coils and increase the number of magnetic lines set up in the magnetic circuit. If the speed is kept constant, the armature conductors cut through the stronger magnetic field at the same speed and thus induce a greater emf and restore the brush potential to its former value. This resistance can be cut out either automatically or by hand.

Shunt-wound generators give a fairly constant voltage, even with varying loads, and can be used for any system which incorporates constant-potential loads. This will operate well in parallel because the voltage of the machines decreases as the load increases. Shunt generators running in parallel will divide the load well between themselves if the machines have similar characteristics.

The necessary change in connections when reversing the direction of rotation of a shunt wound machine is indicated in figure below. Rotation is clockwise when, facing the commutator end of a machine, the rotation is in the direction of the hands of a clock.

Counterclockwise rotation is the reverse. When changing the direction of rotation, do not reverse the direction of current through the field windings. If the direction is reversed, the magnetism developed by the windings on starting will oppose the residual magnetism and the machine will not “build up.”