A particle of mass m having negative charge −q is projected at an angle θ with $$x-axis$$. There exists a uniform electric field E and a uniform magnetic field B along $$x-axis$$. The particle will return to its initial point after n complete revolutions in time t. What is n here?

Question

A particle of mass m having negative charge −q is projected at an angle θ with $$x-axis$$. There exists a uniform electric field E and a uniform magnetic field B along $$x-axis$$. The particle will return to its initial point after n complete  revolutions in time t. What is n here?

Infinity Learn · Accepted Answer

Let particle completes n revolutions in time t, then t $$=$$ nT⇒   $$t=n2$$$$π$$mqBIf particle has to return to its initial point, then displacement along $$x-axis$$ during this time should be zero.Sx $$=$$ uxt $$+12$$  $$axt2$$⇒   $$0=v$$ $$cos$$ θt −$$12$$  qEm $$t2$$⇒  v $$cos$$ θ$$=$$  $$qE2m$$ t⇒  v $$cos$$ θ$$=$$  $$qE2m$$  ×  n $$2$$$$π$$mqB ⇒  n  $$=$$  BvcosθπE

A particle of mass m having negative charge $- q$ is projected at an angle $θ$ with x-axis. There exists a uniform electric field E and a uniform magnetic field B along x-axis. The particle will return to its initial point after n complete revolutions in time t. What is n here?

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A particle of mass m having negative charge −q is projected at an angle θ with x-axis. There exists a uniform electric field E and a uniform magnetic field B along x-axis. The particle will return to its initial point after n complete revolutions in time t. What is n here?

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A particle of mass m having negative charge $- q$ is projected at an angle $θ$ with x-axis. There exists a uniform electric field E and a uniform magnetic field B along x-axis. The particle will return to its initial point after n complete revolutions in time t. What is n here?