You are working in cooperation with the Public Health department to design an el

Question

You are working in cooperation with the Public Health department to design an electrostatic sifter for particles from auto emissions. Particles moving at a speed of V enter one side of the device moving directly toward the opposite side, a distance L away. As the particles enter the box, ultraviolet light is shined on them, knocking electrons off them and giving them each a charge of +Q. Your job is to figure out how large a uniform electric field is needed inside the box so that only particles with a mass larger than M will make it through to the opposite side, with lighter particles remaining trapped inside the box. Express your answer for the magnitude of the electric field in terms of the mass (M), initial speed (V), and charge (Q) of the particles, the length of the box (L), and Coulomb's constant (k). (All letters are uppercase except for k.)

Explanation / Answer

Particles enter from one side and particles with mass larger than M must  ger through.

We assume that the field is applied opposite to the direction of motion.

Both heavy and light particles will face same opposing force.

But the de-acceleration of light particles will be large,

Hence they wil get trapped.

Force acting on particles,  F = QE  (opposite to the direction of their motion)

for a particle of mass m , the acceleration, a = F/m =QE/m

Let, Stopping distance for this particle = d

0 = V2 - 2 (QE/m)d

m = 2QEd/V2

(This formula shows stopping distance is directly proportional to the mass)

Our device must permit all particles of mass above M.

So stopping distance of particles with mass M is L (the box length)

M = 2QEL / V2

=>  E = MV2 /(2QL)    ,  directed opposite to the direction of motion of particles......

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