Magnetism as an Energy Source: Understanding Magnetic Force

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.

Magnetism as an Energy Source Understanding Magnetic Force

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 = \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:

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.

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.

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