{"id":104,"date":"2025-03-02T22:44:02","date_gmt":"2025-03-02T22:44:02","guid":{"rendered":"https:\/\/sebstack.com\/?page_id=104"},"modified":"2026-04-14T14:57:16","modified_gmt":"2026-04-14T14:57:16","slug":"steinmetzs-theoretical-elements","status":"publish","type":"page","link":"https:\/\/sebstack.com\/index.php\/steinmetzs-theoretical-elements\/","title":{"rendered":"Steinmetz’s Theoretical Elements"},"content":{"rendered":"\n

PART I.
GENERAL THEORY.<\/strong><\/p>\n\n\n\n

1. MAGNETISM AND ELECTRIC CURRENT.<\/h3>\n\n\n\n

A magnet pole attracting (or repelling) another magnet pole of equal strength at unit distance with unit force is called a unit magnet pole<\/strong>.<\/p>\n\n\n\n

The space surrounding a magnet pole is called a magnetic field of force<\/strong>, or magnetic field<\/strong>.<\/p>\n\n\n\n

The magnetic field at unit distance from a unit magnet pole is called a unit magnetic field<\/strong>, and is represented by one line of magnetic force<\/strong> (or shortly “one line”) per square centimeter. From a unit magnet pole, a total of [math] 4\\pi [\/math] lines of magnetic force issue.<\/p>\n\n\n\n

The total number of lines of force<\/strong> issuing from a magnet pole is called its magnetic flux<\/strong>.<\/p>\n\n\n\n

The magnetic flux<\/strong> [math] \\Phi [\/math] of a magnet pole of strength [math] m [\/math] is given by:<\/p>\n\n\n\n

[math] \\Phi = 4 \\pi m. [\/math]<\/p>\n\n\n\n

At a distance [math] R [\/math] from a magnet pole of strength [math] m [\/math], and therefore of flux [math] \\Phi = 4 \\pi m [\/math], the magnetic field has the intensity:<\/p>\n\n\n\n

[math] H = \\frac{4\\pi m}{4\\pi R^2} = \\frac{m}{R^2}, [\/math]<\/p>\n\n\n\n

since the [math] \\Phi [\/math] lines issuing from the pole distribute over the area of a sphere of radius [math] R [\/math], that is, the area [math] 4\\pi R^2 [\/math].<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
\"\"<\/figure>\n\n\n\n

In historical physics and engineering literature, especially texts grounded in the CGS electrostatic (ESU) system, one often encounters unit conversions involving seemingly peculiar numerical factors. A notable example is the constant [math]1.11 \\times 10^{-6}[\/math], which appears in equations converting CGS-based capacitance formulas into practical SI-based expressions, particularly when computing capacitance per unit length in coaxial or parallel-wire geometries.<\/p>\n\n\n\n

To understand this factor, we begin with the fundamental conversion between capacitance units:<\/p>\n\n\n\n

From classical sources:<\/p>\n\n\n\n