INTRODUCTION TO ELECTRONICS: The Magnetomotive Force

The relationship between cause, effect, and resistance ( R ) to change are beautifully summed up by the Ohm’s law equation:

( V / R ) = I

The greater the ability a system has to resist change, the less so that change will be observed. As far as Ohm’s law is concerned, change is driven by the energy differential between one place and another. When immobile charged particles give rise to such a system, the presence of electric field lines quantify the system’s ability to impart forces upon other charged species within a given region in space: 

Since work ( J ) is the product of force and distance, the electric field equation can be written in terms of voltage ( V ):

W = Fd

Ed = ( Fd / q )

Ed = ( J / q )

V = Ed

As can be seen diagrammatically and analytically, the ability a capacitor has to impart forces on charged particles is directly proportional to the quantity of E-field lines within the region of space ( dielectric ) between the charged plates. The greater the quantity of field lines, the greater the potential energy ( PE ) of the system. Analogous to to this system is one within which magnetic lines of force have been established within a metallic core:

It is important to realize that neither electric nor magnetic field lines are actual force vectors!!! These lines represent regions of space that will enact a force on charged particles if certain conditions are met. Thus, the potential for a electro-magnetized core to impart a magnetomotive force ( mmf ) is directly proportional to the number of loops ( N ) of current-carrying wire per unit length as well as the magnitude of current ( I ) present:

F_m = NI

Perhaps fittingly, the unit of magnetomotive force is the ampere-turn ( At ). Recall that reluctance ( ℛ ) is the opposition to the establishment of magnetic flux within magnetic materials. Taking the aforementioned factors into account, the Ohm’s law for magnetic circuits takes on the following form:

( F_m / ℛ ) = ɸ

Unlike the Ohm’s law equation, the above equation for magnetic flux is only valid to a certain point. Magnetic circuits can only accommodate so much flux before becoming saturated. A more in-depth discussion of this topic will be covered during subsequent lectures regarding magnetic hysteresis. Additionally, electric current that flows within conductors is created by outside forces, whereas the flux within permanent magnets is created by the internal cooperative positioning of the conductor’s electrons.

Q: A magnetic core is wrapped with 500 turns of a wire that carries 0.3 A of current. If the reluctance of the material is 2.8 x 10⁵ At / Wb, how much flux is established within the magnetic path?

A:

( F_m / ℛ ) = ɸ = ( NI / ℛ )

ɸ = [ ( 500 )( 0.3 A ) / 2.8 x 10⁵ At / Wb ]

ɸ = 5.36 x 10^-4 Wb = 536 µ Wb