Electrons are accelerated from rest through a potential difference of 350V and t

Question

Electrons are accelerated from rest through a potential difference of 350V and then enter a uniform magnetic field that is perpendicular to the velocity of the electrons. The electrons travel along a curved a path with a radius of 7.5cm, because of the magnetic force.

a. what is the magnitude of the magnetic field?

b. estimate the period of this circular path

c. what is the angular speed of this electron?

d. if protons are used instead of electrons, what would be the radius of the path?

e. if the potential difference is increased to 500V, what would be the radius of the electron's path?

Explanation / Answer

eV = 0.5 mv^2=>

v = sqrt (1.6*10^-19 * 350 / (0.5 * 9.1 *10 ^ -31)) = 5*10^6 m/s

Mv^2 / R = Bqv

=> B = mv/qR => B = 9.1*10^-31*5*10^6/(1.6*10^-19*0.075)

=> B = 0.394 mT

T = 2pi * R /v = 90 ns

W = 2 pi /T = 6.93 * 10^7 rad/s

R = 1.6*10^-27 * sqrt ( 1.6*10^-19 * 350 / 0.5 * 1.6 * 10^-27) / 1.6 *10^-19 * 0.394 *10^-3

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