A particle with charge q and kinetic energy K travels in a...

A particle with charge $q$ and kinetic energy $K$ travels in a uniform magnetic field of magnitude $B$ . If the particle moves in a circular path of radius $R,$ find expressions for (a) its speed and (b) its mass.

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Key Concepts

Magnetic Lorentz Force

When a charged particle moves in a magnetic field, it experiences a force known as the Lorentz force. This force is given by F = qvB when the velocity is perpendicular to the magnetic field. The key property is that this force acts perpendicular to the velocity, causing the particle to move in a circular path.

Centripetal Force in Circular Motion

For an object to move in a circular path, there must be a centripetal force that constantly acts towards the center of the circle. For a particle of mass m moving with speed v along a path with radius R, this force is given by F = mv²/R. In the context of a magnetic field, the Lorentz force provides this centripetal force.

Kinetic Energy

A particle's kinetic energy is related to its mass and speed by the relation K = ½ mv². This equation allows for the determination of the speed of the particle if its kinetic energy is known, and it is essential for linking energy to the mechanical properties of the particle.