A positive point charge Q1 = 2.5 ×10^-5C is fixed at the origin of coordinates, and a negative p

step 1 Okay, so for this problem, we have two charges. One's at the origin. I'll call this Q1, and then

A positive point charge Q1 = 2.5 ×10^-5C is fixed at the...

A positive point charge $Q_1 = 2.5 \times 10^{-5}$C is fixed at the origin of coordinates, and a negative point charge $Q_1 = -5.0 \times 10^{-6}$C is fixed to the $x$ axis at $x = +2.4$m. Find the location of the place(s) along the $x$ axis where the electric field due to these two charges is zero.

Transcript

00:01 Okay, so for this problem, we have two charges.

00:04 One's at the origin.

00:06 I'll call this q1, and then another one is over here, 2 .4 meters away.

00:14 So i'll call this distance d, and it has a value of 2 .4 meters, and then q2.

00:23 And then the magnitude of q1 is 2 .5.

00:30 Times 10 of the minus 5 coulombs.

00:36 Coolums.

00:36 Oh my gosh.

00:40 Let me fix this.

00:42 See, make it look a little better.

00:46 Okay.

00:48 So that's the magnitude of q1, and then the magnitude of q2 is 5 times 10 of the minus 6.

00:56 Q2 is negative, but i'm just going to kind of put a negative here and a positive here.

01:00 So we can remember that.

01:03 And then just write down its magnitude.

01:06 And our goal is to find where the electric field is zero.

01:10 I'm just going to double check that that's the prompt.

01:12 Yes, indeed.

01:16 Okay.

01:17 So originally i was like, uh -huh, there's nowhere it's zero because i know the field due to a dipole, and this is basically a dipole, and it's not zero anywhere.

01:25 But alas, q2 is in q1 or not equal, so it's not truly a dipole.

01:32 It's a dipole plus a monopole, which does, which i did find a place where it's zero.

01:39 So let's try to examine like the candidates for where it could possibly be zero.

01:45 So let's note that q1 is bigger than q2.

01:49 And so the field due to q1 is going to be bigger than q2.

01:52 So let's kind of go through and figure out, first of all, in broad strokes, where the field is zero.

01:57 So it could either be to the left of q2 between the two or to the right of q2.

02:01 Let's eliminate the easiest one first.

02:04 So let's consider between here.

02:07 So i'm going to draw these vectors and green to represent the electric field due to each one.

02:11 So the electric field due to q1.

02:15 It's to the right because the electric field is always point away from point charges.

02:20 And then if they're positive, and then towards the point charge if it's negative.

02:25 And so that's from the positive charge.

02:28 And then here's the contribution from the negative charge.

02:32 Which is going to be a bit smaller because it's a smaller charge, but nonetheless to the right...

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