An electron moving with a speed y0 along the positive x -axis at y=0 enters a region of uniform

step 1 In this problem, a proton enters in a uniform magnetic field reason at y equals 0 and with the i

An electron moving with a speed y0 along the positive x...

An electron moving with a speed $y_{0}$ along the positive $x$ -axis at $\mathrm{y}=0$ enters a region of uniform magnetic field $\mathrm{B}^{-}=-\mathrm{B}_{0} \mathrm{k} \wedge$ which exists to the right of y-axis. The electron exits from the region after some time with the speed at co-ordinate y then.

An electron moving with a speed $y_{0}$ along the positive $x$ -axis
at $\mathrm{y}=0$ enters a region of uniform magnetic field $\mathrm{B}^{-}=-\mathrm{B}_{0} \mathrm{k} \wedge$ which exists to the right of y-axis. The electron exits from the region after some time with the speed at co-ordinate y then.

Key Concepts

Conservation of Kinetic Energy in Magnetic Fields

Magnetic forces do no work on moving charged particles because the force is perpendicular to the direction of motion. This principle, stemming from the work-energy theorem, ensures that the speed (and thus the kinetic energy) of a charged particle, such as an electron, remains constant while it moves through the magnetic field, even though its direction of motion may change.

Circular Motion of Charged Particles

When a charged particle enters a uniform magnetic field with a velocity component perpendicular to the field, it experiences a centripetal force as a result of the Lorentz force, causing it to move in a circular path. The radius of this circular motion depends on the mass, velocity, and charge of the particle as well as the strength of the magnetic field.

Lorentz Force

This is the fundamental force acting on any charged particle moving in a magnetic field, given by F = q(v × B). It determines the direction and magnitude of the force experienced by particles such as electrons, and is central to understanding their trajectories in different magnetic field configurations. The cross product nature of the force means that it is perpendicular to both the velocity of the particle and the magnetic field vector.

Uniform Magnetic Field

A uniform magnetic field is characterized by having the same magnitude and direction at every point in the region it occupies. In the context of charged particle motion, a uniform magnetic field produces a consistent Lorentz force on the moving particle, leading to predictable circular or helical motion depending on the initial angle of incidence.

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