Magnetic Circuits

The magnetic circuits discussed here use permanent magnets, however, I consider them to be in the electromagnetic category because the circuits can use electromagnets, permanent magnets, or a combination of both. The purpose of these circuits is to demonstrate concepts in manipulating magnetic fields in order to control the attractive and repulsive forces and to justify further exploitation of the concepts.

Magnetic field shorting repulsive circuit:

In this circuit, two permanent magnets are arranged to repel each other with one magnet mounted on a stationary platform and the second magnet is mounted on the end of a linearly movable shaft or piston. A movable sleeve of high magnetic permeable material (mild steel in this example) is used to “short circuit” the opposing magnetic fields which allows the piston to be pushed close to the stationary magnet with much less force than without the sleeve. With careful positioning of the sleeve, it can be pulled back with relatively little force to allow the magnets to be “open circuited” and repel each other with greater force.

Below are pictures of a test fixture I build to try out this concept. The platform and the piston (the black pieces) are made out of delrin plastic.

Secured to the end of the piston is a piece of mild steel 1/2x1/2x1/8 inch in size which is the same size as each of the two neodymium magnets used. One of the magnets is in the foreground of the picture. It is held on the piston by the attractive force to the steel piece. The other magnet is held in the same way to the steel piece mounted in the center of the platform. The cylinder in the middle of the picture is the sleeve which is made of mild steel and a slot was milled in it to fit over the piston and stationary steel piece. The part on the right is a thin piece of brass used to provide a bearing surface and maintain a small air gap between the sleeve, piston, and the stationary steel piece. The cap head screws holding the platform together are stainless steel (non magnetic). I used plastic for the piston because it has less friction than if it were made from mild steel.

I'm using the following pictures to help show how the pieces fit together and work.

In the picture to the left the magnet is placed on the piston and the piston is placed in the slot on the platform. You can see the piston is hanging out of the back of the platform, this is due to the magnets repelling each other.

The following pictures show the brass bushing and sleeve in place. In the bottom left, the sleeve is in its retracted position allowing the magnets to repel with the same force as without the sleeve. The bottom right shows the sleeve extended to allow the piston to be easily moved closer to the stationary magnet.

You can see that the sleeve does not need to be extended very far to cause the “short circuiting “ of the magnetic fields. I actuate the device by moving the sleeve by hand and observing the forces on the piston. With the sleeve extended, it requires a relatively small amount of force to pull / slide the sleeve back to cause the “open circuiting” and allow the magnets to repel each other. The piston nearly shoots out of the platform. It must be noted that for best performance the sleeve should be extended only far enough to allow the piston to be moved close to the stationary magnet. Otherwise, extending it further will cause the piston to attract to the sleeve before the magnets start repelling each other. If you build one of these for yourself, you will see what I mean.

The Figure 1 below shows the magnetic fields in “open circuit” and “closed circuit” conditions.

Figure 1

Potential Applications:

Reciprocating Motor ( though I believe it would require large strong magnets in order to produce torque that could be used to do work).

Linear Actuator (maybe some kind of manually operated bolt action latch)

Magnetic field summation and cancellation circuit:

This circuit shows how the direction of magnetic fields can sum together to create a large attractive force or can be alternated to cause cancellation and create zero force. The circuit contains two permanent magnets and a plunger, or piston, connected in parallel. An air gap exists between the plunger and the circuit members so that it works in the same way as a plunger in a solenoid. When the magnets are mounted so that their North and South poles are in the same direction, the magnetic fields in the plunger are in the same direction and sum together to create a force on the plunger with the strength of both magnets. When the magnets are mounted so their North and South poles are in opposite directions, the magnetic fields in the plunger are also in opposite directions and the fields cancel each other creating zero force on the plunger. Below are pictures of the test fixture I built to try this out.

The picture on the left is an exploded view of the circuit. I used white-out on the magnets to show which side is North pole. The members of the circuit, and plunger, are made of mild steel square stock 1/2x1/2in. that I got from the local hardware store. The plastic piece in the middle acts as a guide for the plunger and provides an air gap between the plunger and the two lower members of the circuit. I made the plastic piece out of delrin, since I have some delrin scraps, but you could probably find a part at a hardware store that will work after a little modification.

Below are pictures of the circuit assembled in the two configurations. On the left, the magnets have their North poles in the same direction and the plunger is attracted to the top member. The right picture has the magnets mounted so their North poles are in opposite directions and the plunger has zero force on it within the air gap region in the middle of the circuit.

The Figure 2 below shows the behavior of the magnetic fields in both cases.

Figure 2

I am postulating, contrary to popular belief, that in case 2 the magnetic fields do not “link” with each other but form their normal loops and cancel each other in the plunger in the region of the air gap as shown. I hope to obtain a gauss meter to take measurements and prove or disprove this theory.

Potential Applications:

This could be used for motoring but would be most impressive in a generator application.

Discussion of known phenomena and their potential applications (food for thought):

In a magnetic circuit with permanent magnets, the total flux is constant, thus the flux density in a region of the circuit can be increased or decreased by changing the cross sectional area in that region. If the circuit is used to apply force on an armature there must be at least two air gaps to allow movement of the armature (or could be called a plunger as in a solenoid) and the forces on the armature can be altered by changing the area and/or width of the air gaps. There are two types of forces acting in these air gaps, a normal force and a shear force. The normal force acts in-line with the magnetic field (like the plunger in a solenoid) and the shear force is tangent to the alignment of the magnetic field ( like the armature of an electric motor). I believe there could be a way to create a magnetic windmill affect using a combination of different sized air gap areas and widths. This is easier said than done, but I think it is possible. The first example in Figure 3 below shows how the normal force is affected by changing the area of the air gaps.

This is Example 4.4.1 in Furlani, Ref (1), which has been modified to have two air gaps with different size areas.

PM is the permanent magnet and Am is the cross sectional area of PM. The lm is the mean length of the magnetic path and the + x is the convention chosen for positive x direction. We assume the magnetic circuit material has large Um and is not saturated and there is no fringing at the air gaps. Also, we are ignoring the gravitational forces on the armature.

Figure 3

Here we derive the equations for the flux density in each air gap and the force acting on each side of the armature. From equation (8) below, if the air gap lengths x and y are equal the net force on the armature is in the – x direction, F2 > F1, since A1 > A2. If we make the air gap lengths equal and change only the air gap areas, the change in force to change in areas is linear and less than one-to-one. For instance, if A1 = 5(A2), then F2 = 2.69(F1). Bummer, but still may be useful. The relationship of the forces with respect to air gap length is non-linear second order (square in the denominator). So, for the areas in the instance above, we would have to move the armature in the positive x direction by a factor of 1.63 to make F1 = F2 and F = 0. This would be a relatively small change in air gap lengths.

The magnetic shear force is the force that produces the torque on the rotor of an electric motor and in some cases is the force that moves the armature of linear actuators. The Figures 4(a), 4(b) and equations below are from Example 5.8.1 in Furlani, Ref (1), and are shown here for clarification purposes. The equations are derived using the energy approach.

Figure 4(a)                                                                                                                                    Figure 4(b)

The example uses an N turn coil in place of a permanent magnet, however, the force characteristics do not depend on the source of the magnetic field. Here, the energy in the magnetic field, equation (1), is expressed as a function of flux linkage, lambda, and the inductance with respect to position along x direction. We then derive an expression for the inductance, L(x). From this, we are able to derive an expression for the force F.

Equation (6) shows that F increases as x approaches d. In an actual circuit like in Fig 4(a), F would reach a maximum at about x = d and would then decrease as x > d. Also not shown in these equations is that F goes to zero when the armature is fully in the air gap and x < 0, and F becomes positive when the armature begins to exit the air gap in the negative x direction.

Equation (7) shows that the magnitude of F is directly proportional to the width, w, of the armature. This characteristic could be used to manipulate the forces on an armature as it enters and exits an air gap.

So here is some useful information about magnetic circuits. Have fun experimenting!


(1) Edward P. Furlani (2001). “Permanent Magnet and Electromechanical Devices”, San Diego, CA: Academic Press.

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