INTRODUCTION TO ELECTRONICS: Magnetic Field Intensity and Hysteresis

Please recall that the magnetomotive force ( F_m ) equation shows how the magnitude of current ( I ) flowing through ( N ) loops of wire determine how much flux ( ɸ ) is established within a metal core around which the wire is wrapped:

F_m = NI

It is important to remember that the magnetomotive force ( or mmf ) does not represent an actual force, but rather, it represents the potential for forces to be elicited on charges in motion. The ampere-turn ( At ) is the unit used to quantify just how much of such a potential exists within a magnetized core. The relationship between the ( mmf ) of a system and the magnetic flux elicited in the system is as follows:

( F_m / ℛ ) = ɸ

Whereas the magnetomotive force is directly proportional to the quantity of magnetic flux established, the reluctance ( ℛ ) of the conducting material inversely opposes the establishment of flux. We are now ready to express the ( mmf ) of a system in terms of magnetic field intensity ( H ), which is the magnetomotive force per unit length ( l ) of a material:

( F_m / l ) = H

Furthermore, recall the the magnetic flux density ( B ) describes the quantity of flux per cross-sectional area of a material:

( ɸ / A ) = B

Thus, changes in the ( mmf ) of a system change its flux, and changes in magnetic flux elicit changes in ( B ) and ( H ) as well. Fortunately, the relationship between these two quantities is established via usage of a B-H curve, also called a hysteresis curve. The B-H curve demonstrates how certain materials have the ability to retain some magnetic characteristics even after its magnetic field intensity has been reduced to zero!!! This intriguing character that some magnetic materials possess is called retentivity. In order to observe these tendencies, the magnetic field intensity is changed with current reversals within the system at hand, with a reversal of current being enacted by changing the voltage ( V ) polarity of the source. The diagrams that follow are a graphical representation of a hysteresis as described beforehand:

As the magnetic field intensity increases, the magnetic flux density of the material increases as well; however, the amount of flux that can be established within the magnetic path has a saturation point:

Further increases in the value of ( H ) will not increase the flux density at hand. When the magnetic field intensity is decreased to zero, the magnetic flux density will retain a non-zero value somewhere below that of B_sat:

In order to decrease the magnetic flux density to zero, we must continue to apply a reversed magnetic field intensity to the system. Further increases in magnetic field intensity in the opposite direction brings us to another point of magnetic flux saturation:

Yet another reversal in magnetic field intensity will establish a reversal of the trend that has already been observed:

And,

The magnetic field intensities that are required to reduce ( B_sat ) values to zero are called the coercive force values of H_c and – H_c. Materials with low retentivity do not retain a magnetic field very efficiently, whilst those with a high retentivity have ( B_ret ) values that can be very close to ( B_sat )!!! Applications where magnetic flux is involved can either be enhanced or inhibited by a material’s retentivity. For example, the memory cores of a computer’s reader only memory ( ROM ) must be designed and constructed via usage of high retentivity materials. To the contrary, the usage of high retentivity materials in electric car systems would be horribly inefficient if not disastrous and unsafe. The need to reverse current in electric motors occurs most smoothly if newly established flux does not have to compete with pre-existing flux within its hardware.