An electron is projected with an initial speed v_0 = 1.60 time 10^6 m/s into the

Question

An electron is projected with an initial speed v_0 = 1.60 time 10^6 m/s into the uniform field between the parallel plates in Fig. E21.33. Assume that the field between the plates is uniform and directed vertically downward, and that he field outside the plates is zero. The electron enters the field at a point midway between the plates, (a) If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field, (b) Suppose that in Fig. E21.33 the electron is replaced by a proton with the same initial speed V_0. Would the proton hit one of the plates? If the proton would not hit one of the plates, what would be the magnitude and direction of its vertical displacement as it exits the region between the plates? (c) Compare the paths traveled by the electron and the proton and explain the differences, (d) Discuss whether it is reasonable to ignore the effects of gravity for each particle.

Explanation / Answer

a)
let E is the elctric field between the plates.

time taken for the elctrons to cross the plates,

t = d/vox

= 2*10^-2/(1.6*10^6)

= 1.25*10^-8 s

let a is the acceleration of the elctron in uniform elctric field.

dispalcement in y-direction,

y = voy*t + (1/2)*a*t^2

y = 0 + (1/2)*a*t^2

==> a = 2*y/t^2

= 2*0.005/(1.25*10^-8)^2

= 6.4*10^13 m/s^2

now use,

Fe = q*E

m*a = q*E

==> E = m*a/q

= 9.11*10^-31*6.4*10^13/(1.6*10^-19)

= 364 N/c

b) The proton would not hit. Because it has more than electron.

dispalcement of proton in y-direction,

y = voy*t + (1/2)*a*t^2

= 0 + (1/2)*a*t^2

= (1/2)*(q*E/m)*t^2

= (1/2)*(1.6*10^-19*364/(1.67*10^-27))*(1.25*10^-8)^2

= 2.72*10^-6 m

c) As the proton has more mass its acceleration is less.

so, the path of curvature of proton is less than curvature of electron.

d) yes.

acceleration of electron is 6.4*10^13 and acceleration of proton is in the order of 10^13.

the above two values are much larger tnan g(=9.8 m/s^2)

so, gravity can be neglected.

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