A charged plate whose electric field strength E, moving parallel to itself at a speed v, creates a magnetic field of induction B = c2vE. Therefore, when the plate velocity decreases by dv, an "extra magnetic microfield" of induction dB = ±c2(dv)E appears in the surrounding space. Summing up, these "microfields" give an electromagnetic wave, the electric field strength of which depends only on the plate velocity:
Eizl(t, x) = cBizl(t,x) = c2c($\frac{v}{c}_{t-\frac{x}{c}}$)E = ($\frac{v}{c}_{t-\frac{x}{c}}$)E.
The t - cx index means that when calculating the field strength at a distance x from the plate, the value of its velocity should be taken at time t - cx. For example, the electric field strength of radiation from a plate whose velocity is v0 sinω(t-cx) at a distance x from the plate at time t is (cv0)sin[ω(t-cx)]E, since the plate velocity at time t - cx was v0 sinω(t - cx). Prove the validity of the formula Eizl(t,x) = (cvt−cx)E for the case when the velocity v changes as shown in the figures.
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