A charged particle of specific charge (charge/mass) o is released from origin at time $$t=$$ $$0$$ with velocity v→$$=v0(i^+j^)in$$ uniform magnetic field B→$$=B0i^$$. Coordinates of the particle at time $$t=$$π$$/B0$$α are

Correct option is 4v0πB0α,0,-2v0B0α

Questions

A charged particle of specific charge (charge/mass) o is released from origin at time t= 0 with velocity $\vec{v} = v_{0} (\hat{i} + \hat{j})$ in uniform magnetic field $\vec{B} = B_{0} \hat{i}$ . Coordinates of the particle at time t= $π / (B_{0} α)$ are

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v02B0α,2v0αB0,-v0B0α

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0,2v0B0α,v0π2B0α

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detailed solution

Correct option is D

α=qmpath of the particle will be a helix of time period,T=2πmB0q=2πB0α The given time t=πB0α=T2∴ Coordinates of particle at time t=T/2 would be vxT/2,0,-2r Here, r=mv0B0q=v0B0α ∴ The coordinates are v0πB0α,0,-2v0B0α.

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A charged particle of specific charge (charge/mass) o is released from origin at time t= 0 with velocity v→=v0(i^+j^)in uniform magnetic field B→=B0i^. Coordinates of the particle at time t=π/B0α are

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A charged particle of specific charge (charge/mass) o is released from origin at time t= 0 with velocity $\vec{v} = v_{0} (\hat{i} + \hat{j})$ in uniform magnetic field $\vec{B} = B_{0} \hat{i}$ . Coordinates of the particle at time t= $π / (B_{0} α)$ are