It is said that electromagnetic radiation created from accelerated charged particle. I want to mechanically vibrate a charged mass , then will it radiates or not?
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2$\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$– Community BotCommented Oct 7, 2022 at 9:00
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2$\begingroup$ Vibration implies acceleration. Hence a vibrated charge will radiate. $\endgroup$– hdhondtCommented Oct 7, 2022 at 9:24
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2 Answers
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Yes it will. A vibrating particle is accelerating (for example, with acceleration $a = - \omega^2 x$, where $\omega$ is the angular frequency). Hence, since accelerating charges radiate, this vibrating charge will radiate.
It is a typical textbook problem in Electrodynamics to find the power emitted to infinity by such a configuration.
answered Oct 7, 2022 at 9:28
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In electrodynamics the Larmor formula, $P = \dfrac{\mu_0 q^2a^2}{6 \pi c}$, is used to calculate the total power radiated by a non-relativistic point charge as it accelerates.
So consider a spring mass system oscillation with an amplitude of $3\,\rm cm$ with a frequency of $1\,\rm Hz$.
The maximum acceleration $a = (2\pi\times 1)^2 \times 3\times 10^{-2}\approx 1\,\rm m\,s^{-2}$
If the mass has a radius of $1\,\rm cm$ and charged to a potential of $1000\,\rm V$ the charge on the mass, treating it as an isolated spherical capacitor is $q=4\pi \epsilon_0 \times 10^{-2} \times 1000 \approx 1\,\rm nC$.
Thus the maximum power radiated from the system is $P = \dfrac{4\pi 10^{-7}\times (10^{-9})^2\times 1^2}{6 \pi \times 3 \times 10^8} \approx 10^{-35}\,\rm W$!!!
Thus the accelerating charge will radiate but have you the technology to detect it?
