Nikola Tesla's Work In Wireless Power Transmission Page 8

[Sec. 4.b. (1), cont.] Transmitter coils; that is, utilizing no technique of wireless power transmission as described by Tesla. A photograph of this setup also accompanies Tesla's article "The Problem of Increasing Human Energy," Century Magazine, June 1900, pp. 175-211; Figure 7, with the following caption:

"The photograph shows three ordinary incandescent lamps lighted to full candle-power by currents induced in a local loop consisting of a single wire forming a square fifty feet on each side, which includes the lamps, and which is at a distance of one hundred feet from the primary circuit energized by the oscillator. The loop likewise includes an electrical condenser, and is exactly attuned to the vibrations of the oscillator, which is working at less than five per cent of its total capacity."

Let's diagramatically show the situation to scale below and calculate the induced emf from the oscillator:

N₁ = 1 N₂ = 17 f = 100kHg 5% of total capacity = 1,000 amp x 0.05 = 50amp

Calculation of mutual inductance (M) between coils: Refer to Inductance Calculations, Frederick Grover, Dover, New York, 1946, pp. 180-182 for "Mutual Inductance of Coplanar Circular Filaments of Equal Radii" (for distant circles). We will assume two circular coils for simplicity, with a circular coil of diameter equal to a side of the the square loop in the above diagram. This will result in a lower, conservative value for M because the circular coil includes only 80% of of the area of the square coil, but quite acceptable inasmuch as we are looking only for an order-of-magnitude result indication of whether the bulbs could have been fully illuminated by induction effects only.

|M| = 0.001 ((\pi²)/8) (2a/r)³ Da where a=radius of circle in cm r=distance between circle in cm D=constant from table

= 0.001 ((\pi²)/8) (50/150)³ ⋅ 1.116 x 25 x 12 x 2.54, ≈ 0.4 μH for single filaments CONVERSION FACTOR

M_T = M(N₁)(N₂) = 0.4(1)(17) = 0.68μH

For a calculation of the induced emf in the coil containing the three incandescent lamps we assume that Tesla was operating with

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