Three point charges are arranged along the x-axis. Charge q1 = +3.00 is at the origin, and charg

step 1 Hey everyone, this is question number 17 from Chapter 21. In this problem, we're given three poi

Three point charges are arranged along the x-axis. Charge q1...

Three point charges are arranged along the $x$-axis. Charge $q_1 = +3.00 \space \mu$C is at the origin, and charge $q_2 = -5.00 \space \mu$C is at $x =$ 0.200 m. Charge $q_3 = -8.00 \space \mu$C. Where is $q_3$ located if the net force on $q_1$ is 7.00 N in the $-$ $x$-direction ?

Key Concepts

Coulomb's Law

Coulomb's Law provides the fundamental relationship describing the force between two point charges. It tells us that the magnitude of the force is proportional to the product of the absolute values of the charges and inversely proportional to the square of the distance between them. This law is the basis for calculating the forces acting among multiple charges in an electrostatic system.

Superposition Principle

The superposition principle states that the net force acting on any charge is the vector sum of the individual forces exerted on it by all other charges present. This key concept allows us to analyze complex systems by considering each pairwise interaction separately and then summing their contributions to obtain the overall effect.

Force Direction Based on Charge Sign

The direction of the electric force between two charges depends on the signs of the charges involved. Like charges repel, while opposite charges attract. This principle is essential in determining not only the magnitude but also the direction of the force vectors when analyzing the forces in a system of charges.

Transcript

00:01 Hey everyone, this is question number 17 from chapter 21.

00:04 In this problem, we're given three point charges.

00:07 We're told that the net force on q1 is 7 newtons in the minus x direction, and we're asked to find the location of q3.

00:13 So i drew out a little sketch.

00:15 We have q1, we have q2, and then we need to find the direction, the location of q3.

00:24 So we know that the net force is 7 newtons in the minus x direction.

00:28 And if you look at q1 and q2, these are opposite.

00:31 Opposite charges, so they're going to attract and pull this way.

00:35 So in order to have a net charge, we're going to have to have either a positive, well, we're actually told, excuse me, that q3 is minus 8.

00:49 So if we put another negative charge over to the right over here, it would just be more attraction in the right direction, in the positive x direction, and our total force would be in the opposite of what we need.

01:02 Need.

01:02 So that means q3 is going to be somewhere over here because it's a minus charge.

01:09 We just don't know how far.

01:10 This is what we're looking for.

01:12 Okay, so we're working with charges in force, so we have kulam's equation.

01:18 Always good to keep that in mind.

01:19 We have a net force.

01:20 So let's start out by writing an equation for this net force, and that's going to be equal to the force of one on the force of charge two on one and the force of three.

01:32 3 on 1 is going to be added.

01:34 Those are going to be added together.

01:37 So we have kq2 on q1 over r12 squared, radius from 1 to 2 squared.

01:49 And that's pulling in the positive x direction...

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