Inside a cathode-ray tube television set, a beam of electrons is accelerated thr

Question

Inside a cathode-ray tube television set, a beam of electrons is accelerated through a potential difference of 15 kV and aimed at a phosphorescent screen. (a) What is the speed of the electrons? (b) The Earth's magnetic field has a magnitude of 50 T. If the electron beam moves along a path perpendicular to it, how large is the magnetic force on the electron? (c) What is the radius of the helical path that the electron beam follows as a result of its interaction with the Earth's magnetic field? Please show all of your work and relevant formula. Thank you.

Explanation / Answer

a)

using work done by potntial difference is W = 0.5*m*v^2

but W = q*dV = 0.5*m*v^2

1.6*10^-19*15000 = 0.5*9.11*10^-31*v^2

v = 7.258*10^7 m/sec

b) F = q*v*B = 1.6*10^-19*7.258*10^7*50*10^-6 = 5.806*10^-16 N

C) r = m*v/(q*B) = (9.11*10^-31*7.258*10^7)/(1.6*10^-19*50*10^-6) = 8.26 m

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