A particle of specific charge $$qm=$$π $$C/kg$$ is projected from the origin towards positive $$x-axis$$ with a velocity of $$10$$ $$m/s$$ in a uniform magnetic field B→$$=$$−$$2k^T$$. The velocity v of particle after time $$t=112s$$ will be (in$$ $$m/s)

Question

A particle of specific charge $$qm=$$π    $$C/kg$$ is projected from the origin towards positive $$x-axis$$ with a velocity of $$10$$ $$m/s$$ in a uniform magnetic field B→$$=$$−$$2k^T$$. The velocity v of particle after time $$t=112s$$  will be (in$$ $$m/s)

Infinity Learn · Accepted Answer

The particle will move in xy plane in circular path with angular velocity ω$$=$$α$$B=2$$π $$rad/s$$. Therefore angle of rotation $$=2$$π×$$112rad=300$$ v→$$=10$$ $$cos$$ $$30i^$$ $$+$$  $$sin$$  $$30$$ $$j^v$$→$$=10$$ $$32$$  $$i^+12$$ $$j^$$ $$=$$  $$5$$  $$3i^$$  $$+$$  $$j^$$  $$m/s$$

A particle of specific charge $\frac{q}{m} = π C / kg$ is projected from the origin towards positive x-axis with a velocity of 10 m/s in a uniform magnetic field $\vec{B} = - 2 \hat{k} T .$ The velocity v of particle after time $t = \frac{1}{12} s$ will be (in m/s)

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A particle of specific charge qm=π C/kg is projected from the origin towards positive x-axis with a velocity of 10 m/s in a uniform magnetic field B→=−2k^T. The velocity v of particle after time t=112s will be (in m/s)

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A particle of specific charge $\frac{q}{m} = π C / kg$ is projected from the origin towards positive x-axis with a velocity of 10 m/s in a uniform magnetic field $\vec{B} = - 2 \hat{k} T .$ The velocity v of particle after time $t = \frac{1}{12} s$ will be (in m/s)