In a certain cyclotron a proton moves in a circle of radius 0.500 m . The magnitude of the magne

step 1 so the question says that there is a cyclotron in which a proton moves in a circle of radius 0 .

In a certain cyclotron a proton moves in a circle of radius...

In a certain cyclotron a proton moves in a circle of radius 0.500 $\mathrm{m}$ . The magnitude of the magnetic field is 1.20 $\mathrm{T}$ . (a) What is
the oscillator frequency? (b) What is the kinetic energy of the proton, in electron-volts?

Key Concepts

Magnetic Lorentz Force

The magnetic Lorentz force describes the force exerted on a charged particle moving in a magnetic field. According to the equation F = qvB, where q is the charge, v is the velocity, and B is the magnetic field strength, this force acts perpendicular to the velocity of the particle. This perpendicular force causes the particle to move in a circular path, as it continuously redirects the particle's motion without performing work on it.

Cyclotron Frequency

Cyclotron frequency is the rate at which a charged particle orbits in a magnetic field. It is derived by equating the magnetic Lorentz force with the centripetal force required for circular motion, yielding the formula f = qB/(2?m), where m is the mass of the particle. This frequency is independent of the particle's speed and the radius of the orbit, making it a fundamental parameter in the operation of cyclotrons and other magnetic accelerators.

Centripetal Motion in a Magnetic Field

When a charged particle moves in a magnetic field, the magnetic force causes it to travel in a circular path by providing the necessary centripetal force. The relationship between the radius of the path, the particle's velocity, and the magnetic field is given by r = mv/(qB). This concept ensures that by knowing the magnetic field strength and the physical properties of the particle, one can deduce other dynamic properties such as speed and kinetic energy.

Energy Conversion (Joules to Electron-volts)

The kinetic energy of a charged particle is often calculated in joules using classical mechanics; however, in the context of atomic and particle physics, energy is frequently expressed in electron-volts (eV). The conversion factor is defined by 1 eV being equal to 1.602 × 10?¹? joules. This conversion is important for comparing energy scales commonly encountered in accelerators and other experiments in modern physics.

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