Three charges are placed in a straight line as shown in Figure P1.5. FIGURE P1.5 can't copy (a)

Three charges are placed in a straight line as shown in...

Key Concepts

Coulomb's Law

Coulomb's Law describes the force between two point charges. It states that the magnitude of the electrostatic force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. This law is fundamental in calculating the forces when dealing with isolated charges and provides the basis for understanding the interactions depicted in problems involving multiple charges.

Superposition Principle

The Superposition Principle states that when multiple forces act on a charge, the total force is the vector sum of the individual forces exerted by each of the other charges. This principle allows for the separate calculation of forces due to individual pairs of charges, even when more than two charges are involved, and then combining these forces to determine the overall effect.

Vector Addition of Forces

Vector addition is crucial in combining forces that have both magnitude and direction. In the context of electrostatic forces, each force calculated using Coulomb's Law is a vector, and it must be added to the others by considering both the magnitude and the direction, which can depend on the relative positions of the charges and whether the interactions are attractive or repulsive.

Electrostatic Equilibrium

Electrostatic Equilibrium refers to the condition where the net force on a charge is zero. This concept is particularly important in problems where one needs to determine conditions, such as the magnitude and sign of a charge, that will result in balanced forces. Understanding this concept is key to solving problems where forces cancel out, ensuring that a charged particle remains stationary.

Transcript

00:01 In this problem we have three charges all in a straight line and what we want to do is just calculate the force on each of them.

00:07 So let's go ahead and do that.

00:10 So here what we will do is we'll just make the right positive and then the left negative.

00:17 So that's how we'll do this.

00:19 All right.

00:21 So to do all these calculations, what we'll be using is coolans law, which tells you that the force between two charges is this.

00:29 It's coolum's time.

00:30 Constant times the charge of one of them.

00:34 Let's call this q and then the other one, q prime.

00:38 So the charge is between the two or the charge of one particle times the charge of the other particle divided by the distance squared between them.

00:47 Okay.

00:50 And so for our first particle that we're going to look at, q1, we have two forces, right? we have the force due to q2 and we have the force due to q3.

01:01 So the force due to q2 is going to have a force pointed to the left.

01:06 And so we're actually going to have a negative sign on there.

01:10 That's be q, let's see, and then six microculems, and then times 1 .5 microculems.

01:21 And then divided by r squared, which is 3 centimeters squared.

01:28 Now here we do need to note that we need to be careful with units.

01:32 So what we'll do here is convert each of these.

01:36 So one microculum, which you know, is equal to 10 to the negative 6 cullums.

01:43 Right? and so to convert this to coolums, we just multiply this by 10 to the negative 12, essentially.

01:51 And that'll turn both of these into just straight coolums.

01:56 And then similarly, if you want to convert the bottom, it's in three.

02:01 It's in centimeters, we just divide that by 100.

02:05 So this becomes 0 .03 meters squared.

02:10 And that fixes our issues with units, and i'll do the same thing, retro, actively with the q3 term, which is going to be positive direction, and that will be, let's see, 6 times 10 of the negative 6, coolums, and then q3 is 2 .2.

02:31 Times 10 of the negative 6 quons divided by the total distance of 0 .05 meters squared.

02:42 Now here i want to just say that i made this the charge for q3 positive and the only reason for that is because the charge just tells you the direction that the force is taking but we know that the force is pointing this way due to q3 because because, right, this one's positive, the other one is negative.

03:06 And so they're going to have an attraction, attractive force between each other.

03:11 The reason why, in my way of doing this, you wouldn't have a negative here.

03:17 Because normally there'd be like a little vector r hat here, which can kind of confuse things.

03:25 Our hat just points from one charge to the other charge.

03:30 And so the negative would just tell you oh you force to point twice the other charge essentially now plugging in all the numbers what i end up getting is that this is equal to negative 46 .8 newton's and that tells you that this is going to be a magnitude of force 46 .8 newtons pointing to the left just to be a little more explicit...

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