Reluctance.  As the property which opposes the flow of electric current in an electrical circuit is called resistance, so the property which opposes the flow of magnetic lines of force in a magnetic circuit is called reluctance.  In the case of the electric circuit, the resistance is the reciprocal of the conductivity; in the case of the magnetic circuit, the reluctance is the reciprocal of the permeability.  As in the case of an electrical circuit, the amount of flow of current is equal to the electromotive force divided by the resistance; so in a magnetic circuit, the magnetic flux is equal to the magnetizing force or magnetomotive force divided by the reluctance.

[Illustration:  Fig. 90.  Bar Electromagnet]

Types of Low-Reluctance Circuits.  As the pull of an electromagnet upon its armature depends on the total number of lines of force passing from the core to the armature—­that is, on the total flux—­and as the total flux depends for a given magnetizing force on the reluctance of the magnetic circuit, it is obvious that the design of the electromagnetic circuit is of great importance in influencing the action of the magnet.  Obviously, anything that will reduce the amount of air or other non-magnetic material that is in the magnetic circuit will tend to reduce the reluctance, and, therefore, to increase the total magnetization resulting from a given magnetizing force.

Horseshoe Form. One of the easiest and most common ways of reducing reluctance in a circuit is to bend the ordinary bar electromagnet into horseshoe form.  In order to make clear the direction of current flow, attention is called to Fig. 91.  This is intended to represent a simple bar of iron with a winding of one direction throughout its length.  The gap in the middle of the bar, which divides the winding into two parts, is intended merely to mark the fact that the winding need not cover the whole length of the bar and still will be able to magnetize the bar when the current passes through it.  In Fig. 92 a similar bar is shown with similar winding upon it, but bent into =U=-form, exactly as if it had been grasped in the hand and bent without further change.  The magnetic polarity of the two ends of the bar remain the same as before for the same direction of current, and it is obvious that the portion of the magnetic circuit which extends through air has been very greatly shortened by the bending.  As a result, the magnetic reluctance of the circuit has been greatly decreased and the strength of the magnet correspondingly increased.

[Illustration:  Fig. 91.  Bar Electromagnet]

[Illustration:  Fig. 92.  Horseshoe Electromagnet]

[Illustration:  Fig. 93.  Horseshoe Electromagnet]

If the armature of the electromagnet shown in Fig. 92 is long enough to extend entirely across the air gap from the south to the north pole, then the air gap in the magnetic circuit is still further shortened, and is now represented only by the small gap between the ends of the armature and the ends of the core.  Such a magnet, with an armature closely approaching the poles, is called a closed-circuit magnet, since the only gap in the iron of the magnetic circuit is that across which the magnet pulls in attracting its armature.