need some help with a and c auid teait to receive full points. Problem 1. (35 pt

Question

need some help with a and c

auid teait to receive full points. Problem 1. (35 pts) A proton circulates in a cyclotron, beginning approximately at rest at the center. Whenever it passes through the gap between dees, the electric potential difference between the dees is 280 V. The magnetic field in the direction perpendicular to the plane of the spiraling proton is 0.5 T. a) By how much does its kinetic energy increase with each The protons spiral outward in a cyclotron, picking up energy in the gap passage through the gap? (5 pts) Dee Beam b) what is its kinetic energy after it completes 107p Deflector plate through the gap? (10 pts) Oscill c) What is r, the radius of the proton's circular path after t completes those 107 passes? (20 pts) 20 o o based ou AS

Explanation / Answer

a)

increase in kinetic energy = electric potential energy = q V = (1.6 x 10-19) (280) = 4.5 x 10-17 J

b)

kinetic energy after 10 passes = 10 x 4.5 x 10-17 = 4.5 x 10-16 J

c)

kinetic energy after 107 passes

KE = 107 x 4.5 x 10-17

(0.5) m V2 = 107 x 4.5 x 10-17

(0.5) (1.67 x 10-27) V2 = 107 x 4.5 x 10-17

V = 2.4 x 106 m/s

using the formula

r = mV/(qB)

r = (1.67 x 10-27) (2.4 x 106 ) / (1.6 x 10-19 (0.5))

r = 0.0501 m

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