An electron is projected with velocity vec{v} | vedclass

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(A) When a charged particle is projected in a uniform magnetic field at an angle $	heta$ (where $0 < 	heta < \frac{\pi}{2}$),it follows a helical pa

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$\frac{2 \pi m}{eB}$

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(A) When a charged particle is projected in a uniform magnetic field at an angle $	heta$ (where $0 The velocity vector $\vec{v}$ can be resolved into two components: $v_{\parallel} = v \cos 	heta$ (parallel to $\vec{B}$) and $v_{\perp} = v \sin 	heta$ (perpendicular to $\vec{B}$).The perpendicular component $v_{\perp}$ causes the particle to move in a circle,while the parallel component $v_{\parallel}$ causes it to move linearly along the field lines.The velocity vector $\vec{v}$ returns to its initial value after one complete revolution in the circular path. The time taken for one complete revolution is the time period $T$.The time period $T$ is given by the formula $T = \frac{2 \pi m}{qB}$.For an electron,$q = e$,so $T = \frac{2 \pi m}{eB}$.This time period is independent of the angle $	heta$ and the velocity $v$.

An electron is projected with velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$. The angle $\theta$ between $\vec{v}$ and $\vec{B}$ lies between $0^\circ$ and $\frac{\pi}{2}$. Its velocity vector $\vec{v}$ returns to its initial value in a time interval of:

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