In a cyclotron (one type of particle accelerator), a...

In a cyclotron (one type of particle accelerator), a deuteron (of mass $2.00 \mathrm{u}$ ) reaches a final speed of $10.0 \%$ of the speed of light while moving in a circular path of radius $0.480 \mathrm{m}$ What magnitude of magnetic force is required to maintain the deuteron in a circular path?

Key Concepts

Lorentz Force

This is the force experienced by a charged particle as it moves through a magnetic field. It is given by the equation F = qvB, where q is the charge, v is the velocity, and B is the magnetic field strength. In the context of a cyclotron, the Lorentz force acts perpendicular to the particle's velocity, causing it to follow a circular trajectory.

Centripetal Force

For an object in uniform circular motion, a centripetal force is required to keep it moving in a circle. This force is described by F = mv²/r, where m is the mass of the object, v is its speed, and r is the radius of its circular path. In a cyclotron, the magnetic force (Lorentz force) provides the necessary centripetal force.

Cyclotron Operation

A cyclotron is a type of particle accelerator that uses a combination of a static magnetic field and an oscillating electric field to accelerate charged particles. The magnetic field keeps the particles in a circular path while the electric field accelerates them, allowing for controlled manipulation of their trajectories.

Unit Conversion

Accurate problem-solving in physics requires converting measurements into consistent units. This includes converting mass from atomic mass units (u) to kilograms and speeds expressed as a fraction of the speed of light to meters per second, ensuring that all quantities are in SI units for the proper application of formulas.

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