In a linear accelerator, protons are accelerated from rest through a potential d

Question

In a linear accelerator, protons are accelerated from rest through a potential difference to a speed of approximately 3.1 x 106 meters per second. The resulting proton beam produces a current of 2 x 10%u20116 ampere.

a.    Determine the potential difference through which the protons were accelerated.

b.    If the beam is stopped in a target, determine the amount of thermal energy that is produced in the target in one minute.

The proton beam enters a region of uniform magnetic field B, as shown above, that causes the beam to follow a semicircular path.

c.    Determine the magnitude of the field that is required to cause an arc of radius 0.10 meter.

d.    What is the direction of the magnetic field relative to the axes shown above on the right?

Explanation / Answer

Part A)

Apply qV = .5mv^2

(1.6 X 10^-19)(V) = (.5)(1.67 X 10^-27)(3.1 X 10^6)^2

V = 50152 V

Part B)

P = IV

P = (2 X 10^-6)(50152) = .100 W

P = E/t

E = Pt = (.1003)(60) = 6.02 Joules

Part C)

Apply r = mv/qB

.1 = (1.67 X 10^-27)(3.1 X 10^6)/(1.6 X 10^-19)(B)

B = .324 Tesla (32.4 mT)

Part D)
Due to the right hand rule, the direction of the field is out of the page - Positive Z Direction

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