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A non-relativistic enegry particle moves in a transverse uniform magnetic fiel with induction B. Find the time dependence of the particles's kinetic enegry diminshing due to radiation. How soon will its kinetic enegry decrease e-fold? Calculate this time interval for the case (a) of an electron, (b) of a proton. |
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Answer» <P> Solution :`R = (mv)/(eB)`.Then `P = (1)/(4piepsilon_(0))(2)/(3c^(3)) ((eV^(2))/(R ))^(2) = (1)/(4pi epsilon_(0)) (2)/(3c^(3)) ((e^(2)BV)/(m))^(2)` `= (1)/(3piepsilon_(0)c^(3)) ((B^(2)e^(4))/(m^(3))) T` This is the radiated power so `(dT)/(dt)=- (B^(2)e^(4))/(3piepsilon_(0)m^(3)c^(3))T` Intergrating `T = T_(0)e^(-v//TAU)` `tau = (3piepsilon_(0)m^(3)c^(3))/(B^(2)e^(4))` `tau` is `(1836)^(3) ~~ 10^(10)` times less for an electorn than for a proton so electrons radiate away THERI enegry mush fatser in a MEGNETIC field. |
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