Electrons in a beam are accelerated by a voltage of 3.0kV; the beam was then ste

Question

Electrons in a beam are accelerated by a voltage of 3.0kV; the beam was then steered to different points on the screen by coils of wire that produced a magnetic field of up to 0.67T. 1. What is the speed of electrons in the beam? V=__ (give units) 2. What acceleration do they experience due to the magnetic field, assuming that it is perpendicular to their path? What is this acceleration in units of g? a =__ g 3. If the electrons were to complete a full circular orbit, what would be the radius? r =__ (give units) Step by step process would be better than just the answer!

Explanation / Answer

Using conservation of energy:

K.E. = P.E.

1/2 m v^2 = e*Voltage

v = sqrt(2*e*Voltage/m)

v = sqrt(2*1.6*106-19*3*10^3/9.1*10^-31) = 3.246x10^7 m/s

b) F = q v B

m a = q v B

a = q v B / m

a = 1.6*10^-19*3.246*10^7*0.67/9.11*10^-31

a = 3.82x10^18 m/s^2

c) a = v^2 / r

r = v^2/a

r = 2.75529x10^-4 m

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