I took only the introductory electromagnetic course but I couldn't figured out when a single electron accelerated in vacuum which direction it emits electromagnetic waves and is the direction of motion of electron changes, assuming the electric field is along x axis and +x direction. For this question you should only consider the classical case I don't have Quantum electrodynamics background and I'm wondering how classical electrodynamics answers it. If there is a visual representation or an introductory book advise that explains my question I will be thankful for it. Thanks in advance.
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Accelerating charge emits electromagnetic waves in ALL directions. That's why there exists Larmor formula of charge emitted power change over solid angle $\Omega$ : $$ {\frac {dP}{d\Omega }}={\frac {q^{2}}{4\pi c}}{\frac {\sin ^{2}(\theta ),a^{2}}{c^{2}}} $$ But you can try to calculate direction of maximum power - according to extreme finding rules - assign equation to zero, and solve for $\theta$ . – Agnius Vasiliauskas Apr 03 '20 at 08:55
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Also take a look at how and why do accelerating charges radiate electromagnetic radiation question, which may help you. – Agnius Vasiliauskas Apr 03 '20 at 09:09
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@AgniusVasiliauskas thanks for your answer. – asd.123 Apr 03 '20 at 09:10