calculating the strength of a magnet

8/11/2019 Calculating the Strength of a Magnet

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Calculating the strength of a magnet

We're going to start with an electromagnet, to look at how magnets

are measured, because in some ways it is easier to understandelectromagnets first.

Consider the two electromagnets shown above. The one on the rightis a simple coil of insulated copper wire wound around a piece of

iron, such as a nail.The one on the left is the same, but the iron core has been bentaround into the shape of the letter 'C', much like a horseshoemagnet.

The left picture makes it easier to see what is called a magneticcircuit. The coil makes a magnet that has a north and a south pole,and the magnetism moves in a circuit from the north to the south,crossing the air gap to get there.

In this respect, a magnetic circuit is similar to an electrical circuit.The flow always goes from one pole to another, like electricity goesfrom one side of a battery to the other.

Magnetic flux is reluctant to travel through air. It is much easier forit to travel through iron. We say that air has a high reluctance, andiron has a low reluctance. This is similar to resistance in an electricalcircuit.


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In an electrical circuit, we have Ohm's Law, which says that voltageis equal to current times resistance. In a similar way,magnetomotive force is equal to the magnetic flux times thereluctance. Thus magnetomotive force is similar to voltage, and

magnetic flux is similar to current.The magnetomotive force is produced by the coil. It is measured inampere-turns, the electrical current in the coil, measured inamperes, times the number of turns of wire in the coil.

We can calculate the reluctance of the iron core and the air gap ifwe know the length, the area, and thepermeabilityof the iron andthe air. Just like in calculating the resistance of a wire, thereluctance goes down if the cross sectional area gets bigger, andthe reluctance goes up if the length gets longer.

The permeability is a constant that depends on the material.

Thepermeability of free space, also known as the magneticconstant, is0.00000125663706meters kilograms seconds-2amperes-2. Rather than remember all of those clumsy units, wehave a simpler unit, thehenry, and we measure permeability inhenries per meter.

For simplicity, we will refer to permeability as the Greek letter "mu", and the permeability of free space as "mu sub zero", 0, and say

that air is 1 0and iron is about 1,000 0.

The formula for reluctance is the length divided by the product ofthe permeability and the area.

We have an iron core that is one centimeter square in area, and is15 centimeters long, bent into a 'C' shape with a 1 centimeter airgap. The reluctance of the iron core is 15 centimeters divided by1,000 times one square centimeter. The reluctance of the air gap is1 centimeter divided by 1 times 1 square centimeter. We add the

two together to get the reluctance of the entire magnetic circuit.The iron core comes toabout 1.5henries per meter, and the air gapcomes toabout 100.

Now we can calculate the magnetic flux in our magnetic circuit. Fluxis measured in Webers.
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Suppose we have just one loop in our coil, and we have 1 ampere ofcurrent going through the coil. We thus have 1 ampere-turn ofmagnetomotive force.

Dividing one ampere by the total reluctance of the circuit, we

get0.0000000123806607webers.

That is the total flux. We also measure the flux density, that is, theflux per square meter (called B). Webers per square meter is a unitknown as the tesla. We have0.000123806607teslas in the air gapof our our one-turn electromagnet.

If we had 5,000 turns of wire in our coil, we would have 5,000 timesthe flux density, or0.619033035teslas in the air gap of our our5,000-turn electromagnet.

Our little 'C' shaped magnet has room for a coil about 3 centimeterslong and 4 centimeters wide. If we use 28 gauge wire (0.33millimeters in diameter), we can get about 90 turns per layer, andabout 120 layers, for a total of about 10,000 turns. 28 gauge wirecan handle 1.4 amperes of current (more if we cool the coil withwater or liquid helium). So, our magnet is now up to1.7teslas, andruns very hot.

The average length of one turn of wire in our coil is about 10centimeters. We have 10,000 turns, so that is one kilometer of wire.

A kilometer of 28 gauge wire has 213 ohms of resistance. To get1.4 amperes through 213 ohms of resistance takesjust under 300volts.

We have calculated flux and flux density of our coil. Now we needthe magnetic field strength. We start with the magnetomotive forcewe discussed earlier, which is simply the number of ampere-turns inour coil. We have 1.4 amperes, and 10,000 turns, so we have14,000 ampere-turns of magnetomotive force. The magnetic fieldstrength is the magnetomotive force divided by the length of themagnetic circuit, which in our example is 16 centimeters. So themagnetic field strength (called H) is 14,000 ampere-turns/16centimeters, or 875 ampere-turns per centimeter.

So far we have been discussing the 'C' shaped magnet. The simplermagnet works the same way, but the length of the iron core is now
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calculating the strength of a magnet

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