A neutral particle is initially at rest in a uniform magnetic field B as shown in the diagram. The particle then spontaneously decays into two fragments, one with a positive charge +q and mass 3m and the other with a negative charge -q and mass m. Neglecting the interaction between the two charged particles and assuming that the speeds are much less than speed of light, determine the time (in μs) after the decay at which
the two fragments first meet. (use the following data $q = 1 μC, B = 2 πμT, m = 10^{- 15} kg) .$ Both the charges have initial velocities in x-y plane.

Question

Infinity Learn · Accepted Answer

Initial momentum (p) of them will be same but in opposite direction.$$R=pqB$$ $$=$$  same  for  both.Let they meet at angle θ, at time t. Then Rθ$$=v0t$$         (i)and$$       $$R2$$π−θ$$=3v0t$$                     $$(ii)From$$ $$(i) and (ii),   $$t=$$ π$$R2v0$$  $$=$$  π$$2v0$$   $$3mv0qB=$$ $$3$$$$π$$$$m2qB$$  $$=$$  $$3$$π  ×  $$10$$−$$152$$ ×  $$10$$−$$6$$ × $$2$$π  ×  $$10$$−$$6=34$$  ×  $$10$$−$$3$$  s  $$=$$  $$750$$   μs

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