A cyclotron is designed so that the charged particles always circulate in a dee of…

PHYSICS · Subjective · AP · Physics 2: Algebra-based · Magnetism and Electromagnetism · Magnetism and Electromagnetism

Problem

A cyclotron is designed so that the charged particles always circulate in a dee of fixed radius

0.50\,\text{m}

. Protons of charge

e

and mass

m_p

are accelerated from an initial kinetic energy of

1.0\,\text{MeV}

4.0\,\text{MeV}

while remaining inside the same circular orbit. (i) Show that, for a constant orbital radius, the magnetic field required is proportional to the square root of the kinetic energy of the proton. (ii) The magnetic field in the cyclotron is initially

1.5\,\text{T}

when the proton energy is

1.0\,\text{MeV}

. Calculate the magnetic field needed when the proton energy reaches

4.0\,\text{MeV}

. (iii) Determine the speed of the proton at

4.0\,\text{MeV}

and comment, with reason, on whether any relativistic correction is necessary at this energy for routine laboratory calculations.

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