Answer the following questions:

A charged particle enters an environment of a strong and non-uniform magnetic field varying from point to point both in magnitude and direction, and comes out of it following a complicated trajectory. Would its final speed equal the initial speed if it suffered no collisions with the environment?

When a charged particle enters a magnetic field it experiences a force known as Magnetic Lorentz Force which is given by




Now, due to magnetic lorentz force, the particle accelerates so the velocity of particle changes, Magnetic field changes is both magnitude and direction so the Magnitude of Force on particle also keeps on changing, hence the velocity of particle also changes.


Note: Acceleration is Rate of Change of Velocity, so if a particle experiences force, it accelerates and hence its velocity changes. Velocity is a vector quantity so it depends on direction, so velocity of a particle changes if its magnitude or speed changes, direction remain the same, or velocity changes when direction of particle changes and magnitude of velocity or speed remains same, or velocity changes when both speed and direction changes.


In this Case force on the particle is always perpendicular to its velocity, which only changes the direction of the particle and its speed remains same, i.e. velocity of particle changes due to change in direction of particle and magnitude of velocity or speed same as it entered.


Following Figure depict the direction of force on particle at any instant



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