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yxgao
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Why does a uniformly charged sphere that oscillates between two radii at a certain frequency not radiate power?
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yxgao said:Does the radiation only depend on the electric field outside of the sphere? Where can I find the expression of the power radiated?
Why does it not depend on other variables, such as the frequency of oscillation, or the radius?
Thanks for any replies.
yxgao said:So it does not matter that the sphere is constantly changing frequency? I haven't studied this topic in detail before. Is there an online reference that gives an introduction and relevant equations?
Thanks!
If the charge redistributes itself constantly as the radius changes so that [itex] \sigma [/itex] is uniform over the sphere at all times at all radii, there is no time dependent electric field. The only way the charge could redistribute itself that quickly is if the sphere was made of metal.yxgao said:Why does a uniformly charged sphere that oscillates between two radii at a certain frequency not radiate power?
What if the sphere was moving at a speed v?
The reason why a uniformly charged sphere that oscillates does not radiate power is because the oscillations cause the charges to move back and forth in a symmetrical manner, cancelling out any net radiation. This is known as the principle of symmetry and is a fundamental property of electromagnetism.
The principle of symmetry states that any symmetrical system will not radiate energy. In the case of a uniformly charged sphere that oscillates, the symmetrical movement of the charges cancels out any net radiation, preventing the sphere from radiating power.
Yes, the size of the charged sphere does affect its ability to radiate power. A larger sphere will have a larger surface area, which means more charges are involved in the oscillations. This can result in a cancellation of the radiation to a greater extent, making it even less likely for the sphere to radiate power.
Yes, a uniformly charged sphere can radiate power under certain conditions. For example, if the sphere is not perfectly symmetrical or if it is not uniformly charged, it may radiate power due to the asymmetry. Additionally, if the sphere is accelerated at a high enough rate, it can also cause radiation due to the changing electric and magnetic fields.
The principle of symmetry has significant implications for the study of electromagnetism. It helps to explain why certain systems do not radiate power and allows for the prediction and understanding of electromagnetic phenomena. It also plays a crucial role in the development of theories and laws in electromagnetism, such as Maxwell's equations.