In Example 21.4, suppose the point charge on the y -axis at y=-0.30 m has negative charge -2.0

step 1 Hello, everybody. We are back with another question. And this time there's, it's referencing exa

In Example 21.4, suppose the point charge on the y -axis at...

Key Concepts

Coulomb's Law

Coulomb's Law states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This principle is fundamental in electrostatics and is used to calculate how the magnitude of the electric force changes with distance and the amount of charge present, regardless of the charge sign.

Superposition Principle

The Superposition Principle in electrostatics states that the net force on any charge is the vector sum of the forces exerted by all other individual charges. This means that each pair-wise interaction is calculated independently using Coulomb's Law, and then these forces are added together to find the overall force on the charge in question.

Vector Addition of Forces

Since forces are vector quantities, they have both magnitude and direction. When calculating the net force on a charge, each contributing force must be resolved into its components (typically along mutually perpendicular axes), and then these components are summed. This allows for a complete description of the force's magnitude and the direction in which it acts.

Effect of Charge Polarity

The polarity or sign of a charge determines whether the interaction between two charges is attractive or repulsive. When one of the charges changes sign, the direction of the force between it and another charge may reverse, altering the net force on a charge. Understanding how the change in charge polarity affects the overall force is critical when comparing different charge configurations in an electrostatic problem.

Transcript

00:01 Hello, everybody.

00:03 We are back with another question.

00:06 And this time there's, it's referencing example 21 .4 in the book.

00:13 So hopefully you have your book, because i really don't want to write this out or draw this out.

00:20 It's kind of difficult.

00:22 I guess i can try.

00:25 But anyways, in example 21 .4, as you can see in your book, hopefully you're looking at it.

00:32 There's two charges on the y axis.

00:37 One is a positive charge, 0 .3 meters above the origin.

00:47 So i'm going to put this is the origin right here.

00:52 And then there's another positive charge in the example, 0 .3 meters down from that, 3 meters down from the origin.

01:03 But for this problem, it says change that charge.

01:06 Charge to a negative.

01:11 All right and both of the magnitudes are two microculems.

01:21 There's my attempt at writing microculems.

01:28 Oh lord.

01:33 Hold on.

01:34 Give me a second.

01:37 I don't know why this is so hard.

01:43 There you go.

01:44 All right.

01:45 Microculums.

01:46 Big bang, boom.

01:49 And then on the actual origin, so this line right here, 0 .4 meters away.

01:59 Boom.

02:01 There is a positive charge.

02:04 Cachow.

02:06 So that means there is an angle.

02:11 There's going to be angles to this.

02:14 Okay.

02:18 So before we even do anything, let's determine what the forces, what direction the forces are.

02:25 R.

02:26 So let's say this is 1 and 2 and this is big q.

02:35 Good lord, i can't even write q, huh? okay, this is as good as that's going to get.

02:42 Anyways, on on q, one is going to cause a force basically in this direction.

02:50 So in the positive x and negative y direction.

02:55 And that's because they're the same sign so they're going to be pushing away from each other one uq one all right so now that this is negative it's going to be pulling it in so it's going to be a towards it like that so basically we're going to have a negative x and a negative y so what we're going to have here is a i'm putting this in dots because this is the y component of f2 on q.

03:53 Now the thing is, yikes.

03:58 Let me try to, let me just write it real big.

04:03 Maybe that'll help.

04:05 So i want to write a really obnoxiously big just for everybody to understand f2 on q.

04:14 And this is for the y component.

04:17 The y component is downward and the good thing is the one on q y component will be here too.

04:29 So i can just write it again i guess if you want me to do all that, but we get it.

04:43 It's going to be two equal forces due to two different charges but they're equal and they're the same direction.

04:53 So that's the y component.

04:56 Now the y, now the x component of these forces, this f of two on q and the f of one on q over there over here is that one of them is pulling it negative x and one of them is pulling positive x and the magnitudes are all the same.

05:20 Remember, kulom's law, f equals k, which is a constant, and then the q's, and then over r squared.

05:38 So the r's are the same because 0 .3 and 0 .3, and the q's are all the same.

05:45 So that means if we do it just for x, for the x component, they're all the same distance away.

05:54 Point four so if this is pulling it negative x direction this way and we add it to the contribution of this guy onto big q which is pulling it which is pushing it positive x away then adding those together it should look like this let me try to show you in the picture so that first arrow would be f of two on q for the x completely component and then this would be the x component for f of 1 on q so they would cancel each other out does that make sense so that means that for f of x f of x of q is going to be zero i hope that makes sense without me having to do all the calculations and all that just usually using the concepts itself if you break this vector this slanted vector into its components which is basically this and this right x and y component the x component goes that way the y component goes that way but for f of two on q the vector looks like that.

07:38 So the x component looks like that.

07:42 And the y component looks like that.

07:45 So if you look at these two, the x's go in opposite directions.

07:51 So they're going to cancel each other out.

07:53 Only if the numbers are similar, which they are.

07:57 The cues are the same.

07:59 This is a big cue and a two.

08:01 And then for this scenario, for this scenario, and then a big q and a two for this scenario, for two on q...