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Magnetic CircuitAuthor: E.E. Kimberly Magnetism that depends on a flow of electric current is called electromagnetism. Fig. 71 shows a typical magnetic pattern produced by a loosely wound coil or solenoid with air core.
While most of the magnetic flux links all the turns of the solenoid, some of it leaks through, as at a, and does not link the end turns. This is called flux leakage with respect to the end turns. It may be shown by calculation^{1} that, if a solenoid whose length is many times its diameter be wound with N turns uniformly distributed over its length l, the field intensity at its center will be andwhere l = length of solenoid, in centimeters; N = number of turns in solenoid; H = field intensity, in gausses.
If the solenoid were bent so that its axis formed a closed loop, as in Fig. 72, and there were no flux leakage, the amperes required to produce a field intensity H with N turns would be
The flux leakage from such a solenoid or coil may be reduced to an amount negligible for most purposes by substituting for the air core a core of some other material such as iron in which a magnetic field may be established more easily than in air. Thus, for a magnetic circuit all or most of which is in iron, equation (71) may be used except as modified in equation (75). See the solution of Example 71. It is much easier to magnetize iron than a vacuum, or air. The ease with which a material may be made to carry magnetic lines of induction, compared to the ease with which they may be established in a vacuum, is called its permeability. The following comparison may be made between the electric circuit and the magnetic circuit.
If equation (71) were used to find the flux density in the core of a solenoid like that in Fig. 71, which is provided with an iron core of uniformcrosssection and of permeability μ, then
Also, or where ϕ = total flux in the iron; A = crosssectional area of the iron, in square centimeters; I = length of the iron, in centimeters. The term is called reluctance, and its symbol is Ρ (rho). Reluctance in a magnetic circuit corresponds to resistance in an electric circuit. Thus,
or
in which M = magnetomotive force. Equation (76) or equation (77) is called Ohm's Law of the magnetic circuit because of its similarity to the equation of the electric circuit.The resistance of air to low electrical potentials is infinite, and so it is possible to "open" an electric circuit. The reluctivity of air, however, is 1; so it is not possible to have a magnetic path of infinite reluctance and hence, it may be said that a magnetic circuit cannot be opened.


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