# Audel electrical course for apprentices and journeymen - Rosenberg P.

ISBN: 0-764-54200-1

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If a current from a battery is passed through an air-core solenoid as in Figure 12-2, the magnetic lines of force will affect the suspended magnetic needle N. Now, if we provide an iron core for the same solenoid in Figure 12-2, we have iron instead of air for the core. With the same current through the solenoid, the magnetic needle N will be deflected more, although the same magnetizing force was applied to the solenoid. The reason for the greater deflection when the iron core is added is the result of a much increased magnetic flux density B, with the addition of the iron core.

Figure 12-2 Air-core solenoid.

In explanation, suppose that with the air core, the magnetizing force of 50 units of H produced a flux density B of 50 lines of force per square centimeter. The permeability would be B/H = u = 50/50 = 1, which is always true for air. After the addition of the

Laws Governing Magnetic Circuits 141

iron core, we still have 50 units of magnetizing force H, but now have, with 15,000 lines of force per square centimeter,

B 15,000 H ~ 50

300

as the permeability of the iron core that we inserted into the solenoid. This indicates that the iron core conducted 300 times the number of magnetic lines of force as the air core.

Table 12-1 will give you a better idea of the variations in permeability of different substances.

Table 12-1 Permeability of Magnetic Substances

Mmax B

(Gauss/Oersted) (Gauss)

Cobalt 170 3000

Iron-cobalt alloy (Co 34%) 13,000 8000

Iron, purest commercial annealed 6000 to 8000 6000

Nickel 400 to 1000 1000 to 3000

Pennalloy (Ni 78.5%, Fe 21.5%) Over 8000 5000

Perminvar (Ni 45%, Fe 30%, Co 25%) 2000 4

Silicon steel (Si 4%) 5000 to 10,000 6000 to 8000

Steel, cast 1500 7000

Steel, open-hearth 2000 to 7000 6000

Strength of a Magnetic Pole

A unit magnetic pole may be considered to be a point that sends out enough lines of force to produce a flux density of one magnetic line to every square centimeter of a spherical surface situated 1 cm from the pole and centered at the pole point. There will be as many lines of force concentrated at the pole point as there are square centimeters on the surface of a sphere 1 cm in radius. A sphere of 1 cm radius has a surface area of 4w cm2 (12.57 cm2). Therefore, every magnetic pole of unit strength has 4w lines of force emanating from it or entering into it.

Example

A magnet with a strength of 15 unit poles will have 15 X 4w or 189 lines flowing out of the north pole and into the south pole.

142 Chapter 12

Intensity of Magnetizing Force

We have learned that the magnetizing force of an electromagnet is produced by current flowing through a coil of wire. The intensity of this magnetizing force per centimeter of length is expressed as follows:

H 4p IN 1.257 IN

= 10 l = l

where

H = intensity of magnetizing force per unit of length I = current in amperes N = number of turns in the coil l = length of solenoid in centimeters

10 = constant to reduce amperes to absolute units

Magnetic Reluctance

There is resistance to the flow of magnetic lines, called reluctance, the symbol for which is R. No unit term is currently used for reluctance.

The calculation of reluctance is not quite as simple as the calculations of ohmic resistance for electrical circuits. This is due to the peculiar tendency of magnetic substances to reach a saturation point. This indicates that the permeability of a substance is not a fixed quantity, but changes with flux density.

The permeability of a piece of cast iron with a flux density of 4000 lines per square centimeter is 800. It is found that if the flux density is increased to 5000 lines, the permeability will fall to 500.

There are tables available in handbooks for permeabilities of various magnetic substances, under different flux densities. To illustrate our point, Table 12-2 covers one type of wrought iron.

Table 12-2 Flux Density, Magnetic Force, and Permeability

B H m B H m

1000 0.48 2080 9000 2.95 3050

2000 0.61 3280 10,000 4.32 2310

3000 0.78 3850 11,000 6.70 1640

4000 0.92 4340 11,500 9.46 1220

Laws Governing Magnetic Circuits 143

Table 12-2 (continued)

B H M B H M

5000 1.08 4620 12,000 12.40 953

6000 1.20 5000 12,500 16.00 781

7000 1.40 5000 13,000 23.80 546

8000 2.00 4000

The formula for magnetic reluctance is as follows:

R = — s^

where

R = reluctance

l = length of magnetic circuit in centimeters ^ = permeability

s = cross-section of magnetic circuit in square centimeters

This formula indicates that reluctance increases directly with the length of the magnetic circuit and decreases as the product of the permeability and cross-section.

The resistance of a wire increases with the length and decreases inversely with its cross-sectional area and conductivity.

Ohm’s law for an electrical circuit is I = E/R. Rowland’s law for magnetic circuits is fi = mmf/R, or

Magnetic Flux

Magnetomotive Force

Magnetic Reluctance The detailed formula for total flux is fi = mmf/R, or

4p (IN/10) 1.257 IN 1.257 IN ns

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