A particle of specific charge α is projected from origin with velocity v→$$=v0i^-v0k^in$$ a uniform magnetic field B→$$=-B0k^$$. Find time dependence of velocity of the particle.

Correct option is 1v→(t)=v0cosαB0ti^+v0sinαB0tj^-v0k^

Questions

A particle of specific charge $α$ is projected from origin with velocity $\vec{v} = v_{0} \hat{i} - v_{0} \hat{k}$ in a uniform magnetic field $\vec{B} = - B_{0} \hat{k}$ . Find time dependence of velocity of the particle.

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v→(t)=v0cosαB0ti^+v0sinαB0tj^-v0k^

v→(t)=-v0cosαB0ti^+v0sinαB0tj^+v0k^

v→(t)=-v0cosαB0ti^+v0sinαB0tj^-v0k^

v→(t)=v0cosαB0ti^+v0sinαB0tj^+v0k^

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detailed solution

Correct option is A

v→=v0cosθi^+v0sinθj^-v0k^ where θ=ωt=qB0mt=αB0t

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A particle of specific charge α is projected from origin with velocity v→=v0i^-v0k^in a uniform magnetic field B→=-B0k^. Find time dependence of velocity of the particle.

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A particle of specific charge $α$ is projected from origin with velocity $\vec{v} = v_{0} \hat{i} - v_{0} \hat{k}$ in a uniform magnetic field $\vec{B} = - B_{0} \hat{k}$ . Find time dependence of velocity of the particle.