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The magnetic induction in betatron on an equlibrium orbit of radiusr variesduring the acceleration time at paractically constant rate fromzero to B. Assumingthe initial velocity of theelectron to be equalto zero, find: (a) the energyacquired by the electron during the acceleration time, (b) the correspondingdistance covered by theelectronif the accelearation time is equalto Delta t. |
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Answer» Solution :(a) Even in therelativistic CASE, we know that `: p = BER` Thus, `W = sqrt(c^(2) p^(2) + m_(0)^(2) c^(4)) - m_(0) c^(2) (sqrt(1 + (B er//m_(0)c)^(2)) - 1)` (b) The DISTANCE traversed is, `2pi r = (W)/(e Phi) = 2pi r = (W)/(2pi r^(2) eB//Delta t) = (W Delta t)/(Ber)`, on using the result of the previous PROBLEM. |
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