00:04
In this question, a diagram is referenced but not given.
00:08
So i'm going to infer from the problem statement, as it says, regions a and c extend far to the left and right respectively.
00:17
So i'm imagining something like this, with a clear dividing line between the regions.
00:24
And then we have two point charges somewhere in this space, and we're asked if there is a point where the field, the electric field, is equal to zero.
00:37
So we're not necessarily going to have to do the math here.
00:41
We're going to kind of feel our way through it with the concepts, but the formula is important to remember so that we know how the electric field changes.
00:49
If you recall the electric field from a point charge, it's given by kulom's constant, times the charge, divided by r squared.
01:02
And r is the distance between you and the charge.
01:05
It's the distance between the charge and the point where you're measuring the field.
01:10
So in this case, we're not actually going to plug numbers into that result.
01:23
We're just going to use it to kind of discuss how these charges fields will behave.
01:29
So let's take a stab in the dark and say that our first charge is located here, and our second charge is located here.
01:39
So this is one of the possible configurations that i would put on a diagram if i were going to ask a question like this.
01:47
If i were writing something for a class i was teaching, then it would probably involve some boundary, these two charges being the same distance from the boundary.
01:59
So you have this nice symmetric distance here.
02:03
You can call it d.
02:04
You can call it r actually, because that's what's in the formula.
02:07
So why don't we just do that? call that r, call that distance r.
02:17
And then we'll have two charges.
02:19
So why don't we call it q1 and q2? so here's a conceptual piece that's going to help us reduce the number of cases we have to think about.
02:36
When you have two point charges arranged in space, there is kind of a line that they both sit, on.
02:45
There's a single line that they both sit on, which i drew kind of below both of them, but we'll pretend that they sit on that line.
03:00
And on this line, the electric field from each charge is either going to be pointing straight right or straight left.
03:08
So if q1, let's do both positive charges first.
03:12
Let's say this guy is positive, this guy is positive.
03:16
That means the field points away from the point charge.
03:18
So in this case, the field from q1 and again on this line i'm just going to tell you this is the only place where the field can be equal to zero regardless of the size or sign of the charges the line they sit on is the only place the field will be zero so in this case q1's field it's going to point to the right if we're in this middle region here between those two dashed lines kind of in this area anywhere in here on this line in here then the field from q1 is going to point to the right if you're at this point the field points to the right from q1.
03:56
It's always going to point to the right.
03:59
So e1, we could say, for q1, is pointing that way in this region.
04:11
Now, e2, the field from e2, similarly, is pointing away from its point charge, which means in this case it's pointing to the left.
04:24
So if these two charges are the same size, then at the point directly, in the middle between them, this guy right here, the fields are equal and opposite, right? you have e1 from q1.
04:38
Well, it's the same q.
04:41
So looking at the formula up here in the top left, it's the same q and the same r for each charge.
04:47
So it's the same e that you get out, but they're in opposite directions.
04:51
So you have the fields cancelling out right on the boundary, and it's not zero in a or in b.
04:59
So this point where the field is equal to zero is going to kind of move along the line depending on what the charges, sizes, and signs are.
05:11
So we can scroll down and we'll clear some of this up, q1, q2, and the line that they sit on.
05:43
So when both of these are the same sign, or they're both negative, then the field is going to be zero somewhere in here.
05:59
And whichever charge is larger, you can imagine it kind of pushing the zero point away from it.
06:06
So if q1 gets bigger and bigger and bigger, then that zero point is going to, maybe when they're the same size, it'll be right here, directly in the middle between them.
06:18
Symmetry kind of feels right too, doesn't it? if you calculate the field, same q, same r, zero right between them like we just did.
06:26
But now let's let the charge on the left get a little bit bigger.
06:29
Well, that means the field coming from the left is a little bit stronger at this point.
06:33
So now the field there points to the right.
06:36
So we can imagine kind of this point getting shoved to the right as the charge on the left over here is q1 gets bigger.
06:44
And q2 stays the same.
06:45
That zero point is going to move closer and closer to q1.
06:48
But here's the thing.
06:51
It always stays between the two charges because if you get out here, well then the field from q1 points to the right, the field from q2 points to the right, and it'll never be zero because it can't cancel out.
07:05
Same thing happens over here.
07:07
The field from q1 points to the left because it's a positive charge, pointing away from it...