Question

A cyclotron (figure) designed to accelerate protons has an outer radius of 0.333 m. The protons are emitted nearly at rest from a source at the center and are accelerated through 618 V each time they cross the gap between the dees. The dees are between the poles of an electromagnet where the field is 0.792 T. please copy the question in chegg in order to see the figure i didn't know how to upload its the same figure

Answer 1

a)

here by using the formula

Fc = m * v^2 / r = Fb = q * v * B

v = q * r * B / m

and the time period T = 1 / f

v = dr / dt = 2 * pie * r / T

v = 2 * pie * r * f

then

2 * pie * r * f = q * r * B / m

f = q * B / ( 2 * pie * m)

f = ( 1.6 * 10^-19 * 0.792 ) / ( 2 * 3.14 * 1.67 * 10^-27 )

f = 1.208 * 10^7 Hz

b)

v = q * r * B / m

v = ( 1.6 * 10^-19 * 0.333 * 0.792 ) / ( 1.67 * 10^-27 )

v = 2.52 * 10^7 m/s

c)

KE = 0.5 * m * v^2

KE = 0.5 * 1.67 * 10^-27 * (2.52 * 10^7)^2

KE = 5.3 * 10^-13 J

d)

N = KE / ( 2 * q * V)

N = (5.3 * 10^-13) / ( 2 * 1.6 * 10^-19 * 618)

N = 2680