Question

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

• A. vertical circular path with the same speed
• B. horizontal circular path with the same speed
• C. vertical circular path with increased speed
• D. vertical circular path with decreased speed

Hint:

The magnetic force on a charged particle, $\vec{F} = q(\vec{v} \times \vec{B})$, is always perpendicular to both the velocity $\vec{v}$ and the magnetic field $\vec{B}$. Because the force is perpendicular to the velocity, it does no work and cannot change the particle's speed or kinetic energy, only its direction.

Answer 1

The Correct Option is B

The magnetic force on a charged particle is given by the Lorentz force law: $\vec{F} = q(\vec{v} \times \vec{B})$.
Here, the particle is an alpha particle, so its charge $q$ is positive ($+2e$).
The velocity vector $\vec{v}$ is directed towards the east.
The magnetic field vector $\vec{B}$ is directed vertically up.
The velocity vector and the magnetic field vector are perpendicular to each other.
According to the formula for the cross product, the force vector $\vec{F}$ is perpendicular to both $\vec{v}$ and $\vec{B}$.
Using the right-hand rule for a positive charge: Point fingers in the direction of velocity (East). Curl fingers in the direction of the magnetic field (Up). The thumb points in the direction of the force. This direction is South.
The force is initially directed towards the South. The velocity is East. Since the force is perpendicular to the velocity, it acts as a centripetal force, causing the particle to move in a circular path.
The force vector lies in the East-South direction, which is horizontal. Since the force is always in the horizontal plane (perpendicular to the vertical B-field), the particle's motion will be confined to a horizontal circular path.
The magnetic force does no work on the charged particle because the force is always perpendicular to the direction of motion (velocity).
Since no work is done, the kinetic energy of the particle remains constant. Therefore, the speed of the particle remains the same.
Combining these findings, the alpha particle will move in a horizontal circular path with the same speed.