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A beam of non-relatitivistic chagred particles moves withoutdeviation through the region of space A (fig) where there are transervemutuallyperpendicularelectric and magnetic fieldswith streghtE and induction B. Whenthe magnetic field is swichted off, the trace of the beam on the screenSshifts by Delta pi. Knowing the distances a and b, findthe speficchargeq//m of the particles. |
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Answer» Solution :When there is no deviation, `-q vec(E) = q(vec(v) xx vec(B))` or, in scalar from, `E = vB ("as "vec(v) _|_ vec(B))` or, `v = (E)/(B)` .....(1) Now, when the magnetic fieldis swiched on, let the deciationin the field be `x`. Then. `x = (l)/(2) ((q vB)/(m)) t^(2)`, where `t` is the time required to pass through this region. also, `t = (a)/(v)` Thus `x = (1)/(2) ((qvB)/(m)) ((a)/(v))^(2) = (1)/(2) (q)/(m) (a^(2) B^(2))/(E)` ....(2) For the regionwhere thefield is absent, velocity in upward direction `= ((qvB)/(m))t = (q)/(m) aB` ....(3) Now, `Delta x -x = (q aB)/(m) t'` `= (q)/(m) (aB^(2)b)/(E)` when `t' = (b)/(v) = (BB)/(E)` ....(4) From (2) and (4) `Delta x - (1)/(2) (q)/(m) (a^(2) B^(2))/(E) = (q)/(m) (a B^(2) b)/(E)` or, `(q)/(m) = (2 E Delta x)/(a B^(2) (a + 2b))` |
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