2- +--11 points Two parallel plates having charges of equal magnitude but opposi

Question

2- +--11 points Two parallel plates having charges of equal magnitude but opposite sign are separated by 14.0 cm. Each plate has a surface charge density of 35.0 nC/m2. A proton is released from rest at the positive plate. (a) Determine the magnitude of the electric field between the plates from the charge density kN/C (b) Determine the potential difference between the plates (c) Determine the kinetic energy of the proton when it reaches the negative plate (d) Determine the speed of the proton just before it strikes the negative plate km/s

Explanation / Answer

surface charge density is sigma = Q/A = 35*10^-9 C/m^2

a) E = sigma/eo

eo is the permitivity of free space = 8.85*10^-12 N-m^2/C^2

then

E = sigma/eo = (35*10^-9)/(8.85*10^-12) = 3954.8 N/C = 3.95 kN/C

b) V = E*d = 3954.8*0.14 = 553.6 V

c) KE = q*V = 1.6*10^-19*553.6 = 8.86*10^-17 J

d) 0.5*m*v^2 = 8.86*10^-17

0.5*1.67*10^-27*v^2 = 8.86*10^-17

v = 3.25*10^5 m/s
v = 325.74 km/s

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