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“Lines of force” can best be explained with an illustration. The photo shows the lines of magnetic force created with a magnet. A piece of paper sits atop the

What are magnetic lines of force?
Photo of bar magnet with north pole on left and south on right. Iron filings reveal lines of force. [Image source: Common domain. https://en.wikipedia.org/wiki/Magnetic_field Retrieved Sept. 5, 2017.]
magnet, and iron filings are scattered on the paper. We are looking at the pattern created by the iron filings on the paper, not directly at the magnet (which lies underneath the paper).

As school children know, if we give the filings a little shake to overcome the friction of the paper’s surface, the magnet reaches out to the iron filings and arranges them into lines. As to why lines are formed, rather than, let’s say, a blurry solid, that’s not something I can answer.

Magnetic Lines of Force and the Magnetic Field

The lines of force are not the magnetic field, itself. The lines of force only reveal the underlying magnetic field. This idea is similar to the idea of physical manifestations making visible an underlying emotion like anger. The physical manifestations might be the person shouting and their face turning red. But these are merely indicators of the chemical changes occurring within their body and their raging subjective experience of “feeling angry.”

Electrical Lines of Force

What are electrical lines of force?
Electrical lines of force of a proton (left) and electron (right). [Image source: Geek3 – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=10568742 Retrieved from https://en.wikipedia.org/wiki/Electric_charge Sept. 5, 2017.]
The accompanying diagram shows electrical lines of force, which are drawn as symbols of the underlying field. While this is only a symbolic drawing, it is possible to make the lines of force of electrical fields visible. One way involves generating electrical fields in a liquid and dropping powders into it that trace out the lines of force. Making the lines of force visible in an electrical field is more difficult than for magnetic lines of force.

History of Lines of Force

“Lines of force” is a concept first introduced by the great experimental physicist, Michael Faraday (1791-1867). Later, James Clerk Maxwell gave mathematical expression to Faraday’s concept. These physicists saw the lines of iron filings as indicative of an underlying “magnetic fluid.” “Fluid” is used here in the technical sense of a substance that takes the shape of its container, either a liquid or a gas. However, Faraday and Maxwell did not know what the physical nature of this fluid might be.

Michael Faraday -- who was Michael Faraday
Michael Faraday, 1842, by Thomas Phillips [Image source: https://en.wikipedia.org/wiki/Michael_Faraday Retrieved Sept. 11, 2017.]
The invisible magnetic fluid is strongly present around a magnet. We can feel this fluid resisting when we try to force the north poles of two bar magnets together. As these scientists saw it, at greater and lesser strengths, the magnetic fluid would fill all of space.

Similarly, Faraday and Maxwell envisioned electrical fluid surrounding electrically-charged matter. Today, we would call these magnetic and electrical substances “fields” rather than “fluids.”

James Clerk Maxwell - who was James Clerk Maxwell
James Clerk Maxwell by George J. Stodart [Image source: The Scientific Papers of James Clerk Maxwell, Ed: W. D. Niven; Dover, New York, 1890. Public Domain, https://commons.wikimedia.org/w/index.php?curid=2311942; https://en.wikipedia.org/wiki/James_Clerk_Maxwell Retrieved Sept. 11, 2017.]
The concept of fields replaces the Newtonian concept of action-at-a-distance. In the Newtonian conception, matter acts on other matter without touching, but through a distance. As a note, Newton made it clear that he was dissatisfied with this concept but relied on it because it was supported by experimental results and mathematical calculations.

Faraday’s and Maxwell’s concept of field is widely accepted today. In Quantum Field Theory, the quantum field is considered by physicists to be the most fundamental component of nature, its basic building block.

For more information on electrical and magnetic fields, see force field.