Question1 Two extremely large (disk shaped) parallel plates are laying in the ya

Question

Question1 Two extremely large (disk shaped) parallel plates are laying in the ya-plane, separated by a distance of 0.25m. Each plate has an equal but opposite charge density of magnitude 5.7x 10 °Cm2. At tOs you fick a tiny bead of mass 41 x 10kg through a very small hole in the center of the negatively charged plate so that it leaves your finger with a net charge of 2.1 x 10" and a velocity of -8.5m/si42m/s j, heading toward the positive plate You can ignore the etfects of gravity in this problem.

Explanation / Answer

Given

separation of the plates is s = 0.25m

Magnitude of charge density of each plate is sigma = 5.7*10^-6 C/m2

so the magnitude of electric field between the plates is E = sigma /epsilon not = (5.7*10^-6)/(8.854*10^-12) N/C = 643776.8240 N/C

now the force acting on the bead is F = E*q = ma ==> a = E*q/m

initial velocity of the bead is vi = (-8.5 m/s i + 4.2 m/s j), magnitude is Vi= sqrt((-8.5)^2+4.2^2) m/s = 9.481 m/s

mass of bead is m = 4.1*10^-2 kg, charge of bead is q = 2.1*10^-6 C

the velocity of the bead when it reaches the positive plate is

using equations of motion vf^2 - vi^2 = 2*a*s

vf^2 = vi^2+ 2*a*s

= 9.481^2 +2*((643776.8240*2.1*10^-6)/(4.1*10^-2))(0.25)

vf^2 = 106.37632844390

vf = sqrt(106.3763284439) m/s

vf = 10.314 m/s

kinetic energy of the bead by the time it hits the positive plate is k.e = 0.5*4.1*10^-2*10.314^2 J = 2.181 J

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