The magnetic field in a cyclotron is 0.50 T. What must be the radius of the vacuum chamber if t

step 1 In this given problem in cyclotron the magnitude of magnetic field is 0 .50 Tesla. Maximum proto

The magnetic field in a cyclotron is 0.50 T. What must be...

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Key Concepts

Lorentz Force

The Lorentz force is the force exerted on a charged particle moving through a magnetic field. It is given by the equation F = q(v × B), where q is the charge, v is the velocity, and B is the magnetic field. In the context of the cyclotron, this force causes the particle to move in a circular path when its velocity is perpendicular to the magnetic field.

Centripetal Force and Circular Motion

For a particle to travel in a circular path, a centripetal force is required, which is given by F = mv²/r, where m is the mass, v is the velocity, and r is the radius. In a cyclotron, the magnetic Lorentz force provides this centripetal force, leading to the relationship r = mv/(qB). This relationship is fundamental in determining the necessary size of the particle’s circular path, such as the radius of the vacuum chamber.

Cyclotron Operation

A cyclotron is a type of particle accelerator that uses a static magnetic field to bend the trajectory of charged particles while an alternating electric field accelerates them. The balance between the Lorentz force and the required centripetal force allows the cyclotron to maintain the particles on spiral paths, gradually increasing their energy until they reach a desired velocity.

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