2. A beam of protons is fired into a rectangular region of space that contains a

Question

2. A beam of protons is fired into a rectangular region of space that contains a uniform magnetic field. The protons are moving due East and the field points straight down (see diagram). The speed of the protons in the bean is 2.3 × 106 m/s. The magnitude of the field is 2.44 × 10-3 T. The width of the rectangular region (West to East) is d beam (a) What is the magnitude of the force on a single proton when it first (b) What is the maximum value of d for which the proton beam will make (c) Describe the motion of the proton beam (in as much detail as possible) enters the magnetic field region? it through to the other side of this rectangular region? if d is larger than this maximum value. Also describe the motion of (X the electron beam if d is smaller than this value.

Explanation / Answer

a) Force F = q*v*B = 1.6*10^-19*2.3*10^6*2.44*10^-3 = 8.97*10^-16 N

b) d = 2*r

r is the radius of the circle ,which is path followed by the proton

r = (m*v)/(q*B) = (1.67*10^-27*2.3*10^6)/(1.6*10^-19*2.44*10^-3) = 9.84 m

d = 2*r = 2*9.84 = 19.68 m

c) since velocity is perpendicular to the magnetic field ,then it takes the circular path

for proton .if d is larger ,then proton will complete a circle in the given wirdth

for electron and given width is smaller than this value then electron doesnot complete the circle

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