Cyclotron The cyclotron (figure above) is a device used to accelerate elementary

Question

Cyclotron The cyclotron (figure above) is a device used to accelerate elementary particles such as protons to high speeds. Particles start at point A with some initial velocity and travel in circular orbits in the magnetic field B. The particles are accelerated to higher speeds each time they pass in the gap between the metal "Dees," where there is an electric field E. (There is no electric field within the cavity of the metal Dees.) The electric field changes direction each half-cycle so that the particles are increased in speed at each passage through the gap. Let's assume that we are accelerating protons, q =+e. The potential difference between the plates is deltaV. If the particle starts on the surface of the bottom 'Dee' with zero initial velocity then what is velocity of the proton when it enters the top 'Dee'? Based on our understanding of motion of charged particle in B field we know that the particle will undergo a circular motion and exit the top 'Dee'. Remember that B field only changes the direction and there is NO change in the speed of the particle. What is the magnetic force on the proton? The magnitude of the centripetal acceleration is related to the tangential speed; alpha=nu^2/gamma Use the magnetic force and centripetal acceleration to calculate the tangential speed nu. How much distance did the proton travel in the upper 'Dee'? When the proton exits the upper 'Dee' the direction of the E field is reversed so that the proton will accelerate again. Show that the kinetic energy of the particles increases by 2qdeltaV each revolution, assuming the gap is small. Explain your reasoning.

Explanation / Answer

a) Velocity of Proton in upper D = qBr/m

b) Magnetic force = qvB

c) distance travelled in upper D = pi* r

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