A particle of specific charge q / m = pi text | vedclass

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(D) The time period of a charged particle in a uniform magnetic field is given by $T = \frac{2 \pi m}{q B}$.Given $q/m = \pi 	ext{ C kg}^{-1}$ and $B

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$5(\sqrt{3} \hat{i} + \hat{j})$

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(D) The time period of a charged particle in a uniform magnetic field is given by $T = \frac{2 \pi m}{q B}$.Given $q/m = \pi 	ext{ C kg}^{-1}$ and $B = 2 	ext{ T}$,we have:$T = \frac{2 \pi}{\pi 	imes 2} = 1 	ext{ s}$.The particle is projected along the $X$-axis. After time $t = \frac{1}{12} 	ext{ s}$,the angle of deviation $	heta$ is given by:$	heta = \frac{t}{T} 	imes 360^{\circ} = \frac{1/12}{1} 	imes 360^{\circ} = 30^{\circ}$.Since the magnetic field is in the $-\hat{k}$ direction,the particle moves in the $XY$-plane and deflects towards the positive $Y$-axis.The velocity vector $\vec{v}$ at time $t$ is given by:$\vec{v} = v_0 (\cos 	heta \hat{i} + \sin 	heta \hat{j})$$\vec{v} = 10 (\cos 30^{\circ} \hat{i} + \sin 30^{\circ} \hat{j})$$\vec{v} = 10 (\frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j}) = 5(\sqrt{3} \hat{i} + \hat{j}) 	ext{ ms}^{-1}$.

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