Two positive point charges, each of which has a charge of 2.5 ×10^-9 C, are located at y=+0.50 m

step 1 Okay, so this one is a little bit of a complex problem. We have three point charges arranged as

Two positive point charges, each of which has a charge of...

Key Concepts

Symmetry in Electric Fields

Symmetry in the arrangement of charges simplifies the analysis of electric forces. When charges are symmetrically arranged around a point, certain force components may cancel out due to equal magnitude and opposite direction. Recognizing symmetry helps reduce complexity and focus on the non-canceling components, facilitating easier computation of the net electric force.

Coulomb's Law

Coulomb's law describes the magnitude and direction of the electric force between two point charges. It states that the force is proportional to the product of the charges and inversely proportional to the square of the distance between them, with the force directed along the line connecting the charges. This law forms the basis for calculating the interaction between any pair of charged particles.

Superposition Principle

The superposition principle in electrostatics states that the total electric force on a charge due to multiple other charges is the vector sum of the individual forces exerted by each of those charges separately. This concept allows for evaluating complex systems by considering one charge interaction at a time and then summing up the forces.

Vector Addition of Forces

Vector addition is crucial when combining forces since both magnitude and direction must be considered. When forces act at angles, they can be decomposed into perpendicular components (typically horizontal and vertical), added separately, and then recombined to determine the overall resultant force. This method is essential for analyzing the net impact of multiple forces acting concurrently.

Transcript

00:01 Okay, so this one is a little bit of a complex problem.

00:04 We have three point charges arranged as such in space.

00:07 We have two charges that are 2 .5 times 10 to the negative 9 coulumes.

00:12 They're positive.

00:13 One is at negative 0 .5.

00:15 The other one's at 0 .5.

00:16 This here is the origin 0.

00:18 And then we have one on the x -axis, which is 0 .7 meters away from the origin.

00:23 And that one is 3 .0 times 10 to the negative 9.

00:27 And the question is, what is the total force acting on? on this particular charge.

00:33 Now, we're only focused on what's happening on this charge.

00:37 So i'm just going to draw a quick force diagram.

00:41 They're all positive charges, which means they're going to repel each other.

00:44 So this charge is going to feel a force that way from this charge.

00:50 We'll call this one, we'll call this two, and we'll call this three.

00:54 So one on three is going to make it go that way.

00:56 And then two on three is going to make it go that way at the same angle.

01:00 And so that's going to be kind of a setup for later.

01:06 Now, the first thing we have to do is we have to use kulms law, which is force is equal to k constant times q1.

01:14 We'll do one and three first, divided by the separation distance between one and three squared.

01:20 So we're looking for this distance, which we don't know off the top of our heads, but we know this is 0 .5 and we know this is 0 .7.

01:28 So we can actually use pythagram theorem to figure this out.

01:32 So 0 .5 squared, because this is the right triangle.

01:36 So 0 .5 squared plus 0 .7 squared is equal to c squared, or r squared, i guess i should call it.

01:42 And that'll tell us what r is.

01:44 When you plug that in the calculator, you end up getting 0 .86 meters.

01:49 So that's what we're going to use for our r.

01:51 So let's go ahead and calculate this now, the magnitude of the force.

01:55 So k is 9 times 10 to the 9.

01:58 That's a constant that's just given to you.

02:00 The first charge is 2 .5 times 10 to the negative 9.

02:04 And the second charge is 3 .0 times 10 to the negative 9...

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