Technical Article

# Magnetism as an Energy Source: Understanding Magnetic Force

April 30, 2021 by Alex Roderick

An invisible force occurs between two magnets when they are brought close to each other. This force may be an attraction force that pulls the magnets together or a repulsion force that pushes them apart. See Figure 1. Magnetic force is expressed in dynes. A dyne is a force that produces an acceleration of one centimeter per second per second on 1 gram of mass.

Figure 1. Like poles of a magnet repel and unlike poles of a magnet attract. A unit of magnetic force is equal to one dyne between the poles of two magnets separated by one centimeter. Image courtesy of Encyclopedia Britannica.

The force between two magnetic poles is similar to the force that exists between two charges. In both cases, the force can be one of attraction or repulsion. In the 1780s, Charles-Augustin de Coulomb, a French physicist, developed the mathematical formula for calculating the force for either case. His law for magnetic poles states that the force between two magnetic poles is directly proportional to their magnetic strength and inversely proportional to the square of the distance between them. For example, if a force of 10 dynes exists between two magnetic poles separated by 1′′ of air, a force of 160 dynes would exist if the poles were 1⁄4′′ apart. Based on the inverse square law, the force would increase 16 times. Conversely, if two magnetic poles were 2′′ apart, a force of 2.5 dynes would exist. At twice the distance, the force would be one-fourth as strong. The equation for this relationship is as follows:

$F&space;=&space;\frac{m_{1}xm_{2}}{d^{2}}$

where

F = force (in dynes)

m1 = strength of first magnetic pole (in unit magnetic poles)

m2 = strength of second magnetic pole (in unit magnetic poles)

d2   = distance between poles (in cm)

A unit magnetic pole is a force of one dyne between two magnetic poles separated by a distance of 1 cm. One pound-force is 444,822 dynes, making one dyne an extremely small force. The force between magnetic poles is affected by the medium between the poles. For a medium other than air, the permeability (μ) of the medium must be included in the calculation. Coulomb’s law addresses a basic principle, but it is not commonly used to calculate magnetic force. The equation becomes:

## Magnetic Fields

A magnetic field is an invisible field produced by a current-carrying conductor, a permanent magnet, or the Earth that develops a north and a south polarity. The English physicist Michael Faraday was the first scientist to visualize a magnetic field as a state of stress consisting of uniformly distributed lines of force (magnetic flux). Magnetic lines of force are the invisible lines of force that make up a magnetic field. See Figure 2. The magnetic field surrounding a magnet has a greater density at the poles and radiates out into the space surrounding the magnet in a symmetrical pattern.

Figure 2. A magnetic field is the invisible field produced by a permanent magnet that develops a north and a south polarity. Image courtesy of CMPCO Magnetic Products

The more magnetic lines of force present in a given cross-sectional area, the greater the force and flux density. Flux density is the measure of the magnetic lines of force per unit area taken at right angles to the direction of flux. If the unit of length is a centimeter, then the flux density is measured in gauss. A gauss is a unit of flux density equal to one magnetic line of force per square centimeter. Flux density is expressed by the following equation:

$F&space;=&space;\frac{m_{1}xm_{2}}{\mu&space;d^{2}}$

where B = flux density

φ = total number of magnetic lines of force

A = cross-sectional area (in cm2)

The magnetic field surrounding a bar magnet can also be plotted using a compass. A compass aligns itself with the magnetic lines of force at each position. The compass needle rotates a full 360° as it is moved from one pole of the magnet to the other. The movement of the compass pointer also shows that magnetic lines of force have direction.

Just as the north pole of a magnet is defined in terms of the Earth’s field, the direction of magnetic lines of force is also defined. By definition, the magnetic lines of force travel from the north pole to the south pole of the magnet. This is the polarity of the magnetic field. The magnetic lines of force travel from the south pole to the north pole inside the magnet to complete the loop.

## Understanding Electromagnetism

Magnetism and moving electrons are closely related to each other. The three phenomena pertaining to electromagnetism are:

• Moving electric charges produce magnetic fields.
• Magnetic fields exert forces on moving electric charges.
• Changing magnetic fields in the presence of electric charges cause electrons to flow

In 1820, Danish physicist Hans Oersted noted that electron flow produces a magnetic field. He had a current-carrying conductor pointing in a north-south direction. A compass was near the wire. He noted that, in the absence of electron flow, the alignment of the wire and the alignment of the compass needle were the same. However, each time the circuit was closed to allow electron flow, the compass needle aligned itself at a right angle to the conductor. See Figure 3. When the direction of electron flow was reversed, the compass needle pointed in the opposite direction while maintaining a 90° displacement to the conductor.

##### Figure 3. With a current-carrying conductor pointing in a north-south direction, the needle of a compass aligns parallel to the conductor with no electron flow and perpendicular to the conductor with electron flow.

Oersted’s findings led to speculation that the magnetic field of a magnet may interact with the magnetic field created by the flow of electrons through a conductor.

## Magnetism Applications

Magnetism is used in a wide variety of applications in modern industry. The ability of an electric current to create a magnetic field is used in generators, electric motors, and solenoids. See Figure 4.

##### Figure 4. Magnetism is one of the most important mechanisms of producing electrical energy and is used in a wide variety of applications. Image Courtesy of  SolPass

Regardless of the basic sources of potential energy that drive them, generators provide most of the electrical energy consumed. A generator (alternator) is a machine that converts mechanical energy into electrical energy by means of electromagnetic induction. Some of the common sources of potential energy used to drive generators include falling water, fossil fuels, and nuclear energy. A motor is a rotating device that converts electrical energy into mechanical energy. The torque (rotating mechanical force) on a motor shaft is used to produce work.

Electromagnetism made possible the invention of power tools. The variety of tools available include devices to drill, strike, saw, grind, sand, turn, cut, shape, and form materials. Power tools have taken much of the labor out of many tasks that previously could only be achieved through human power.

Magnetic radiation plays a large role in modern medicine. X-ray, CAT (computer-assisted tomography) scans, and MRI (magnetic resonance imaging) are a few of the applications. MRI began to be used in the early 1980s as a noninvasive way to see images of thin slices of the body. This is accomplished by measuring the characteristic magnetic behavior of specific nuclei in the water and fats of the body. These images help identify normal, damaged, and diseased tissue.

Another important use of electromagnetism is the generation of magnetic fields using an electrical current. Electromagnets are used as substitutes for permanent magnets in many applications. Advantages of electromagnets over permanent magnets are that the strength of electromagnets can be varied by varying the amount of electron flow, and the magnetism can be turned off by turning off the electron flow.

The advancement of the wave theory of electromagnetic radiation set the stage for modern communications. Electromagnetic fields of various frequencies make modern communications possible. Electron flow in a conductor results in a radiating magnetic field, and this field induces a current into any conductor it comes into contact with. Radio, television, and microwave transmissions of all types operate on this theory. Transmitters emit electromagnetic radiation from their antennas, and the signal induces the information into the antenna of the receiver.

## Summarizing Energy Sources

Electrical energy can be created from friction, pressure, light, heat, chemical reactions, and magnetism. Friction creates electrical energy when two different types of materials are rubbed together. Pressure applied to piezoelectric materials produces a voltage directly proportional to the amount of applied strain. Some materials emit electrons when exposed to light and are used as a mechanism of converting light into electricity. Heat can also be used to generate electrical energy through the Seebeck or Peltier effect. Chemical reaction was the first reliable and usable method for producing electrical energy and is used in today’s batteries. Magnetism is the most commonly used mechanism of producing electrical energy. The relative motion between a magnet and a conductor is used to produce AC electricity.