## Basic Motor Theory (6)

Energy Conversion To produce voltage, it is necessary to move a conductor through a magnetic field as stated above. Mechanical energy is required to provide motion to this conductor. With the field energy remaining constant, the conductor is changing mechanical energy into electrical energy.
Voltage Generation There is a definite relationship between the direction of the magnetic flux, the direction of motion of the conductor and the direction of the induced EMF. Figure 1 shows the motion of the conductor perpendicular to the magnetic field. The voltage and current output are perpendicular to both the motion of the conductor and the magnetic field.

Figure 1. Voltage Generation

To illustrate this with Fleming’s right hand rule, the thumb and first two fingers of the right hand are extended at right angles to one another, the thumb will indicate the direction of motion of the conductor, the forefinger will indicate the direction of the magnetic field, and the middle finger will indicate the direction of voltage or current.
Applying this rule, one can see that the current will reverse if the motion of the conductor changes from down to up. This is true even though the magnetic field does not change position. Therefore, the rotating coil in Figure 2 will produce a voltage which is continually changing direction.

Figure 2. Revolving Coil in a Magnetic Field

Voltage Induced in Conductor Moving Through a Magnetic Field
Revolving Coil in a Magnetic Field
The coil in position AB, in figure 2, encloses the maximum amount of flux. The flux decreases as the coil moves toward position CD and becomes zero at CD, since the plane of the coil is parallel to the magnetic field. Then the flux increases in the opposite direction, reaching a negative maximum at BA and diminishing again to zero at DC. The flux reverses and increases again in the original direction to reach a maximum at AB.
Although the flux is maximum at positions AB and BA and zero at positions CD and DC, the induced EMF will be maximum at positions CD and DC and zero at positions AB and BA. This is true because the EMF depends upon the rate of change of flux or rate of cutting flux lines and not upon the quantity enclosed.
If the coil in Figure 2 were rotated at a constant speed in a uniform magnetic field, a sine wave of voltage would be obtained. This is shown in Figure 3 where both the amount of flux enclosed and the EMF induced are plotted against time.

Figure 3. Voltage Sine Wave Produced by rotation of a coil at constant speed in a uniform magnetic field.
Value of Generated Voltage The EMF at any instant of time is proportional to the number of turns in the coil times rate of change of flux. The C.G.S. (centimeter gram second) unit of EMF known as the abvolt is defined as that value induced, in a coil of one turn, when the flux linking with the coil is changing at the rate of one line or Maxwell per second; or as that value induced when magnetic flux is being cut by the conductor at the rate of one line per second. A volt is equal to 108 abvolts or an abvolt is equal to 10-8 volts. Therefore, the instantaneous value of voltage is expressed as:
e = N x (d / dt) x 10-8
where:
e = voltage
N = the number of turns
d / dt = the rate of change of flux
This equation can be further developed to obtain the voltage for movement of a conductor at constant velocity through a uniform magnetic field:
E = N B v sin x 10-8
where:
E = voltage
N = number of turns
B = flux density in lines per square inch
= length of the conductor in inches
v = velocity in inches per second
= the angle between the conductor and flux field
If the conductor moves directly across the field at right angles to it, then = 90° and sin = 1. The equation then becomes:
E = N B v x 10-8
It should be noted that this equation is a special form of the original equation and is not applicable in all cases.