Consider the parallel plates as shown above. Assume that the injected particles

Question

Consider the parallel plates as shown above. Assume that the injected particles are polystyrene beads, each of mass 2.0 x 10^-11 g; the beads carry negative charges of hundred to thousands of elementary charges. The uniform electric field between the plates is E = 900 N/C as shown. The uniform field region is L = 19 cm long and d = 1.0 cm wide. The particles have initial velocity = 3.0 m/s and enter the corner of the field region at theta = 5.0 degrees. Ignore the effects of gravity. What is the maximum number of elementary charges for which the beads exit the field region without striking one of the plates?

Explanation / Answer

For maximum no. of elementary charges, the bead will just hit the lower plate

=> Range = L
v^2 sin (2) / a = L

=> a = v^2 sin (2) / L

a = 3^2*sin(10 degrees) / 0.19

a = 8.22543999475 m/s^2

Now, acceleration, a = F/m = qE/m

q = ma/E = (2*10^-14 kg)*(8.22543999475)/900

q = 1.8278756*10^-16

no. of elementary charges = q/e = 1.8278756*10^-16 / (1.6*10^-19) = 1142 ( approximately)

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