Three point charges are arranged on a line. Charge q3 = +5.00 nC and is at the origin. Charge q2

step 1 Hey everyone, this is question number 13 from Chapter 21. In this problem, we are given three po

Three point charges are arranged on a line. Charge q3 =...

Key Concepts

Coulomb’s Law

Coulomb’s Law quantifies the force between two point charges. It states that the magnitude of the electrostatic force between two charges is proportional to the product of the absolute values of the charges and inversely proportional to the square of the distance between them. This principle is fundamental to calculating interactions between point charges in vacuum or air, and it provides the mathematical framework needed to determine forces in various charge configurations.

Superposition Principle

The superposition principle in electrostatics states that the net force acting on a charge due to a collection of other charges is the vector sum of the individual forces exerted by each of those charges independently. This concept is critical when dealing with multiple charges, as it allows for the analysis of complex interactions by adding up the contributions from each charge to find the overall effect.

Electric Force Direction and Charge Sign

The direction of the electric force between two charges depends on the signs of the charges. Like charges repel each other while opposite charges attract. This concept is essential because, when determining equilibrium or net forces, one must consider both the magnitude and the direction of each force, which are dictated by the interactions between positive and negative charges.

Electrostatic Equilibrium

Electrostatic equilibrium refers to the state where the net force acting on a charge is zero, meaning there is no resulting acceleration. For a system of charges, achieving equilibrium typically involves balancing forces such that the attractive and repulsive interactions cancel each other out. In problems like the one presented, setting the net force to zero is a key step in calculating an unknown charge required to balance the other forces in the system.

Transcript

00:01 Hey everyone, this is question number 13 from chapter 21.

00:04 In this problem, we are given three point charges on a line.

00:09 We're given q1 is at 2 centimeters, q2 is at 4 centimeters with a charge of minus 3 nanoculams, and q3 is a charge of plus 5 nanoculams, and is at the origin.

00:25 And then we're also told that the net force on q3 is zero, so q3 is not moving.

00:30 And then we're asked to find the magnitude and sign of q1.

00:33 So my first suggestion when you do these kind of problems is to draw out a sketch of the situation like i have.

00:38 So we have q3 at the origin, q1, q2, we're solving for q1.

00:42 So first, let's just take a second to think about this problem and what's going on with these two charges.

00:48 Or with the three charges.

00:50 So we're asking about q1 is going to have a force.

00:55 Exerted on or whereas we're talking about q3 excuse me being stationary have the force is zero so q3 has the force exerted on it by 1 and it has the force exerted on it by 2 so the force exerted on it by 2 is opposite so that's going to be that's going to be attractive so that means that if it's at zero and it's not moving we can we can go ahead and make the guess that q1 is going to be positive charge because q2 is going to pull it toward and q1 is going to push it away and that's going to be that's going to hold it in tension, hold q3 stationary.

01:36 So if we have it stationary, that means that the force of 1 on 3 is equal to the force of 2 on 3.

01:51 And as you see over here, i went ahead and wrote out kulam's equation as a reminder because that's what we're dealing with is forces with charges.

01:58 So we have these two statements and we can go ahead and write out these equations.

02:03 So force of one on three is going to be k, q1, q3 over r squared, and that's going to be equal to k, q2, q3 over r squared...

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