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The speed light maybe determined by an electrical circuit using low frequency ac fields
only. Consider the arrangement shown in the Fig. (4). A sinusoidally varying voltage
V₀ cos(2Ï€ft) is applied to a parallel plate capacitor C1 of radius a and separation s and
also to the capacitor C2. The charge flowing into and out of C2 constitutes the current
in the two rings of radii b and separation h. When the voltage is turned off the two sides
(the capacitor C1 on one side and the rings on the other) are exactly balanced. Ignore
wire resistance, inductance and gravitational effects.
(a) Obtain an expression for the time-averaged force between the plates of C1.
(b) Obtain an expression for the time-averaged force between the rings. The magnetic
force between the two rings maybe approximated by those due to long straight wires
since b >> h.
(c) Assume that C2 and the various distances are so adjusted that the time-averaged
downward force on the upper plate of C1 is exactly balanced by the time-averaged
downward force on the upper ring. Under these conditions obtain an expression for
the speed of light.
(d) Numerically estimate the speed of light given that: a = 0.10 m, s = 0.005 m, b =
0.50 m, h = 0.02 m, f = 60.0 Hz, C1 = 1.00 nF (nano Farad) and C2 = 632 μF
(micro Farad).
[Hint: Not all the given quantities are required to obtain the estimate.]