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An electron carries an electric charge. A stationary electron creates no magnetic field. (Like a wire with no current). An electron moving at constant velocity generates a steady magnetic field, but (like a stationary magnet in a coil of wire) a constant magnetic field won't result in another electric field. An electron moving with a changing velocity (ie. accelerating), however, generates a changing magnetic field, which will produce a changing electric field, which produces a changing magnetic field, etc. In other words, it generates an electromagnetic wave.