00:01
From part a, we know the acceleration is going to be equal to zero, so the velocity is either going to be zero or moving at a constant.
00:07
And the only two forces are the drag forces and the electric field forces.
00:15
And these perfectly must balance out.
00:18
And so qe is the electric force here.
00:24
And the drag force, we're told, is k times r times v.
00:30
And so we can shift things around here.
00:33
I'm going to divide by an r and an e, and i get q over r is equal to kv over e, which is what part a wanted us to show.
00:47
Now, taking the previous equation we just found, and i'm going to solve for v, and when i do that, i get v as equal to eq over kr, and we know this is a constant since the acceleration is not changing, or the acceleration is zero, so v is not changing.
01:08
In other words, it's a constant.
01:11
And so if v is a constant, we can use the formula that the velocity is equal to the distance traveled over the time.
01:17
And then rearranging this for x, i get x is equal to the velocity times of time.
01:21
This is only valid if v is a constant.
01:25
And now, just plugging in v, i get eq over kr, and then the time is t.
01:32
It's given in the problem.
01:35
And then now this is just equal to et over k.
01:40
And then i have q over r here.
01:42
And this is what part b wanted us to show.
01:49
In part c, we're looking at changing the factor of q over r.
01:53
And so let me just rewrite the result...