3. (25 points) A capacitor is created by placing two large rectangular sheets of

Question

3. (25 points) A capacitor is created by placing two large rectangular sheets of metal in parallel. Initially thereis a vacuum between the plates and the plates are connected to a 12.0 V battery. Each sheet has a total area of A 1.50 m2 and is separated by a distance d 0.500 mm (5.00 x 104 m) +0 AreaA a. What is the capacitance of this pair of parallel plates? b. If a proton is placed on the positive plate, how fast will it be travelling if it is allowed to strike the negative plate? (Hint: Work and Potential Energy)

Explanation / Answer

part(a)

capacitance C = eo*A/d = 8.854*10^-12*1.5/(5*10^-4) = 2.66*10^-8 F

part(b)

work done = change in KE

V*q = (1/2)*m*(vf^2-vi^2)

12*1.6*10^-19 = (1/2)*1.67*10^-27*(vf^2 - 0^2)

vf = 4.79*10^4 m/s

part(c)

newcapacitance Cnew = k*c

K = dielectric constant of rubber = 6.7

new capacitance Cnew = 6.7*2.66*10^-8 = 17.822*10^-8 F

part(d)

charge Q = Cnew*V = 213.8*10^-8 C

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part(e)

energy stored U = (1/2)*C*v^2 = (1/2)*17.82*10^-8*12^2 = 1.283*10^-5 J

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