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$$ μ$$s) after the decay at whichthe 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

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$$ μ$$s) after the decay at whichthe 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.

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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