(a) Capacitor with proton. Two large parallel plates are separated by 0.75 cm an

Question

(a) Capacitor with proton. Two large parallel plates are separated by 0.75 cm and carry uniform charge densities equal in magnitude and opposite in sign. A proton is between the plates and has an acceleration of magnitude 1.39 x 1011 m/s2. Find the charge density on the plates. Note that proton mass is 1.7 x 10-27 kg.  (2 points) (b) Capacitor with ionized argon atoms. In an optics experiment, a discharge tube is filled with singly ionized argon atoms, each having a mass of 6.64 x 10-26 kg. If the electric field inside the tube is 7500 N/C, find the acceleration of each argon ion. (3 points)

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Explanation / Answer

(a)
Acceleration of the proton, a = 1.39 * 10^11 m/s^2
Mass of proton, m = 1.7 * 10^-27 Kg
Charge of Proton, q = 1.6 * 10^-19 C

Force on the Proton, F = m*a = q*E
E = (1.7 * 10^-27 * 1.39 * 10^11 )/(1.6 * 10^-19) N/C
E = 1476.9 N/C

Let is the surface charge density.
E = /eo
= 1476.9 * 8.85 * 10^-12 C/m^2
= 1.31 * 10^-8 C/m^2

(b)
m = 6.64 * 10^-26 Kg
E = 7500 N/C
Q = 1.6 * 10^-19 C

F = m*a
q*E = m*a
1.6 * 10^-19 * 7500 = 6.64 * 10^-26 * a
a = 1.81 * 10^10 m/s^2
Acceleration of each argon ion, a = 1.81 * 10^10 m/s^2

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