Here are the essential concepts you must grasp in order to answer the question correctly.
Cyclotron Motion
Cyclotron motion refers to the circular motion of charged particles in a magnetic field. When a charged particle, such as a deuteron, moves perpendicular to a magnetic field, it experiences a magnetic force that acts as a centripetal force, causing it to travel in a circular path. The radius of this path is determined by the particle's speed, charge, and the strength of the magnetic field.
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Magnetic Field Strength
The magnetic field strength (B) is a measure of the magnetic force experienced by a charged particle moving through the field. In a cyclotron, the magnetic field is crucial for maintaining the circular motion of the particles. The relationship between the magnetic field strength, the charge of the particle, its velocity, and the radius of the circular path is given by the equation B = (mv)/(qR), where m is the mass, v is the velocity, q is the charge, and R is the radius.
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Cyclotron Frequency
Cyclotron frequency is the frequency at which a charged particle orbits in a magnetic field. It is directly proportional to the magnetic field strength and the charge of the particle, and inversely proportional to its mass. The formula for cyclotron frequency is f = (qB)/(2πm), where f is the frequency, q is the charge, B is the magnetic field strength, and m is the mass of the particle. This frequency is essential for determining the conditions under which the cyclotron operates effectively.
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