A 6.0-MeV (kinetic energy) proton enters a 0.20-T field, in...

Key Concepts

Lorentz Force

The Lorentz force is the fundamental force experienced by a charged particle moving in a magnetic field. It is given by the vector equation F = q(v × B), where q is the charge, v is the velocity vector, and B is the magnetic field vector. This force is always perpendicular to both the velocity of the particle and the magnetic field, which causes the particle to undergo circular motion when the velocity is perpendicular to the field.

Circular Motion of Charged Particles

When a charged particle moves in a magnetic field, the Lorentz force acts as a centripetal force, causing the particle to follow a circular path. The centripetal force required to maintain this circular motion is provided entirely by the magnetic force. This relationship forms the basis for analyzing the motion of charged particles in devices like cyclotrons and mass spectrometers.

Kinetic Energy and Speed Relation

The kinetic energy of a moving particle is related to its speed through the equation KE = ½ mv². When the kinetic energy is known, as in the case of a high-energy proton, its speed can be computed. This speed is crucial for further calculations, especially when determining the radius of the circular path in a magnetic field, since the centripetal force depends directly on the particle's velocity.

Cyclotron Radius

The cyclotron radius is the radius of the circular path of a charged particle moving perpendicular to a magnetic field, and it can be calculated using the expression R = mv/(qB). This equation ties together the mass, velocity (derived from kinetic energy), charge of the particle, and strength of the magnetic field. It is a central formula in understanding the motion of charged particles in magnetic fields and has important applications in particle accelerators and plasma physics.

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