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The cyclontron'soscillator frequency is equlal to v = 10 MHz. Findthe effectivevoltageappliedacross the doesof thatcyclotron if the distance betweenthe neighbouring trajecroies of protonsis not less thanDelta r = 1.0 cm, withthe trajectoryradius beingequal to r = 0.5 m. |
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Answer» SOLUTION :We know that for acharged particle (proton) in a magnetic field, `(mv^(2))/(r) = B EV` or `mv = BER` But, `omega = (eB)/(m)`, Thus `E = (1)/(2) mv^(2) = (1)/(2)m omega^(2) r^(2)`. So, `Delta E = m omega^(2) r Delta r = 4pi^(2) v^(2) mr Delta r` On the hand `Delta E = 2 eV`, where`V` is the effective acceleration voltage, across the Does, therebeing two CROSSINGS PER revolution. So, `V ge 2pi^(2) v^(2) mr Delta r//e` |
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