A point particle, mass of 450 micrograms and electrical charge of -256e, is fall

Question

A point particle, mass of 450 micrograms and electrical charge of -256e, is falling vertically at a constant rate in an electric field that exists between two oppositely charged metal plates. What is the smallest magnitude and direction of an electric field that can be applied to stop the particle from falling so that it remains stationary? Give your answer in the form “a.bc x 10^(y) N/C, up/down”. Although it has not been asked for, you should give some thought to which plate would be positively charged and which would be charged negatively. (i.e., is the upper plate positive or negative compared to the lower plate, to enable the problem to be carried out?)

Explanation / Answer

The force due to gravity Fg = mg and the force due to electric field Fe = qE

So there are only two forces working on the particle and since the aim is to stop the particle,

the net force on particle must be zero.

So Fg = qE

The smallest magnitude of the electric field,

E = mg/q = 450*10^-6*9.81/(256*1.6*10^-19) = 1.08*10^14 N/C

Now coming to the direction,

Since the electric force must be in up direction, but here the charge in negative so the electric field must be downwards.

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