A negative charge of -0.550 μC exerts an upward 0.600 N force on an unknown charge that is loca

A negative charge of -0.550 μC exerts an upward 0.600 N...

Key Concepts

Coulomb's Law

Coulomb's Law is the fundamental principle that describes the force between two point charges. It states that the magnitude of the electrostatic force (F) between two charges is directly proportional to the product of the absolute values of the charges and inversely proportional to the square of the distance (r) between them. This law is mathematically represented as F = k|q1q2|/r², where k is the Coulomb constant. It is essential for calculating the magnitude of forces in problems involving electrostatic interactions.

Electrostatic Force and Charge Interactions

Electrostatic forces depend on the magnitude and sign of the interacting charges. Like charges repel each other while opposite charges attract. The direction of the force between two charges is determined by these interactions, meaning that if a negative charge exerts an upward force, it indicates that the other charge must have the sign necessary to create an attractive interaction, based on the setup. Understanding these relationships is crucial for analyzing the directions of forces in such problems.

Newton's Third Law

Newton's Third Law states that for every action, there is an equal and opposite reaction. In the context of electrostatics, this means that if one charge exerts a force on another, the second charge exerts a force of equal magnitude but in the opposite direction on the first. This concept is essential when computing or verifying the forces between two charged particles, ensuring that the forces are balanced and mutually consistent.

Transcript

00:02 Hello, everybody.

00:03 We are back with another question, and this one says, a negative charge of negative 0 .55 microculems exerts an upward 0 .6 newton force on an unknown charge that is located 0 .3 meters below, directly below the first charge.

00:22 So we have a negative charge.

00:25 Let me draw it out real quick.

00:26 There's a negative charge, and it's q.

00:34 Is equal to negative 0 .055.

00:44 Oh, whoops, that 0 is not supposed to be there, actually.

00:49 I read that wrong.

00:51 It's just negative .55 micro.

00:55 Oh, hold on.

00:58 Let's been a little, let me get back into this point.

01:04 55 micro.

01:07 Kulums.

01:07 There we go.

01:12 Another way of writing that.

01:13 Let me write in scientific notation.

01:17 Maybe that'll be better.

01:22 Actually, let's just write it in terms of kulams.

01:26 We don't have to move the decimal or anything yet.

01:30 Let's not try to confuse ourselves too much yet.

01:35 Right? anyways.

01:37 Alright, so we're setting up.

01:39 So this is the first part of it.

01:40 Of the question just says this is our charge that we know and it is 0 .3 meters away.

01:48 0 .3 meters that is our r from another charge over here and the charge is feeling an upward force so that means it has to be a positive force because an upward force on this charge right here q2 would mean there is an attractive force between the two charges, the two particles.

02:22 So we know the sign.

02:25 Now what it asks us, i want to write out the force real quick, sorry.

02:34 What it asks us to do is find the magnitude of this charge.

02:39 And the force was 0 .6 newtons.

02:45 All righty.

02:45 So now you guys remember from multiple problems now, we have the kulom's law.

02:52 F equals kqq over r squared.

02:59 So q1, q2 over r squared.

03:06 Now the thing is, when you write this equation, sometimes they don't put this in the book, and sometimes they do, and sometimes they just don't mention it, et cetera, et cetera, you're going to have the absolute value of these charge values.

03:25 So for q1 and q2, you're actually in the equation, you're just using the magnitudes of them.

03:32 You're not using the negative part or the positive part.

03:36 So for this problem, particularly, since this is a negative charge, usually you would see a negative, but we just look at the magnitude and not the negative part.

03:53 Right the interesting thing is they described the forces upwards so another way of referencing the force and then and as a result not needing the absolute values would be if this charge felt a negative force you can say it felt a negative force that means it was being pulled inward from to the other um to the other particle.

04:33 And that makes sense when you do the math, right? because if you have a negative here and then the other charge would be positive, you'd end up with an overall negative value for your force.

04:45 So then the force that this feels, as well as this one on each other, would be negative.

04:53 The force is negative towards the other one.

04:56 It's not a positive force away.

04:59 Does that make sense? but in the for this question particularly, we're just going to try to keep it more simple, describe this as an upward force, which we then realize is towards, and we're just going to use the magnitudes of each charge instead of worrying about the sign.

05:22 So anyways, what we're going to do is solve for q2.

05:26 So we're going to go bow, q2, is f over k, r squared over q1.

05:46 Cool...

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