An alpha particle moving with a certain speed | vedclass

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(B) The force on a charged particle moving in a magnetic field is given by the Lorentz force formula: $\vec{F} = q(\vec{v} 	imes \vec{B})$.Here, the

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a horizontal circular path with the same speed

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(B) The force on a charged particle moving in a magnetic field is given by the Lorentz force formula: $\vec{F} = q(\vec{v} 	imes \vec{B})$.Here, the velocity $\vec{v}$ is towards the east (let this be the $+x$ direction) and the magnetic field $\vec{B}$ is directed vertically up (let this be the $+z$ direction).The direction of the force is given by the cross product of $\vec{v}$ and $\vec{B}$. Using the right-hand rule, $\hat{i} 	imes \hat{k} = -\hat{j}$.Thus, the force acts towards the south ($-y$ direction).Since the force is always perpendicular to the velocity, the particle moves in a circular path. Because the force is horizontal (in the $xy$-plane), the particle will move in a horizontal circular path.Furthermore, since the magnetic force does no work on the charged particle, its speed remains constant.

An alpha particle moving with a certain speed towards the east enters a uniform magnetic field directed vertically up. The alpha particle will then move in:

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