Question

You reproduce Thompsons e/m experiment by applying an accelerating voltage of 295 V to the apparatus. (a) At what fraction of the speed of light do the electrons move? (b) If the deflecting electric field has a magnitude of 8.0·10⁶N/C, what is the strength of the magnetic field? (c) If the beam radius r is measured to be 5 cm, what must be the strength of the magnetic field produced by the Helmholtz coils? Hint: you know the value of e/m.

Answer 1

given
V = 295 V

we know, q = 1.6*10^-19 C

m = 9.1*10^-31 kg

a) Workdone on the electron = gain in kinetic energy

q*V = (1/2)*m*v^2

==> v = sqrt(2*q*V/m)

= sqrt(2*1.6*10^-19*295/(9.1*10^-31))

= 1.018*10^7 m/s

= 1.018*10^7/(3*10^8)

= 0.0339*c <<<<<<<<------------------Answer

(here c is light speed)

b) for no deflection

Fb = Fe

q*v*B = q*E

B = E/v

= 8*10^6/(1.018*10^7)

= 0.786 T <<<<<<<<------------------Answer

c) we know, r = m*v/(B*q)

B = m*v/(r*q)

= 9.1*10^-31*1.018*10^7/(0.05*1.6*10^-19)

= 1.16*10^-3 T <<<<<<<<------------------Answer