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## Homework Statement

Suppose I drop a ball from high enough in the sky that, at some point, it reaches terminal velocity. At this point, the ball is no longer accelerating. It is traveling at a constant velocity. Does this mean that at terminal velocity, the force of gravity on the ball is equal to the force of air resistance (viscousity)? A net force of zero?

If so, then what is going on in Millikan's Oil drop experiment? A particle drops between two plates. Suppose the plates are not electrically charged. Then at some point, the falling particle will reach terminal velocity, at which point the force of gravity on the particle will equal the force of air resistance.

However, when the plates are then electrically charged, the particle is then decellerated (assuming the particle is negative and the top plate is positive). When the particle comes to a complete stop, the electrical force attracting the negative particle upward is exactly equal to the force of gravity pulling the particle downward. So once again, a net force of zero?

So is it that as the electrical charge of the plates are increased, the total upward force on the particle is greater than the total downward force? And this would be why the particle is slowing down (or accelerating upward) until coming to a complete stop.

I am trying to imagine to "quantify" the relationship that is occurring between the downward force of gravity, the upward force of air resistance, and the upward force of the positively charged top plate.

Intuitively, if feels as though the downward force of gravity always remains the same (9.8m/s^2), the air resistance decreases while the electric charge of the plates increase. But if the force of air resistance decreased by the same quantity as the increase of the force of the charged plates, then the particle would remain falling at a constant speed. Therefore, I would guess that there is some sort of relationship between the upward forces as one force increases and the other decreases so as to slow the particle down to a complete stop.

What would be that relationship between the upward forces of air resistance and electrical charge of the plate?

## Homework Equations

## The Attempt at a Solution

Not homework, just self study.