Two charges, one of 2.50μC and the other of -3.50 μC, are placed on the x -axis, one at the orig

Two charges, one of 2.50μC and the other of -3.50 μC, are...

Key Concepts

Equilibrium in Electrostatics

Equilibrium in electrostatics exists at a point where the net force on a charge is zero. At this point, the individual forces from surrounding charges cancel each other out completely. Finding such a point often involves setting the magnitudes of the forces from the different charges equal and solving for the position, taking into account the distances and the nature (attractive or repulsive) of the interactions.

Effects of Charge Sign

The sign of a charge determines whether the interaction between two charges is attractive or repulsive. Like charges repel and opposite charges attract. Understanding the influence of charge sign is crucial when determining the direction of forces acting on a test charge and consequently finding the point of equilibrium.

Coulomb's Law

Coulomb's Law describes the electric force between two point charges. It states that the magnitude of the force is directly proportional to the product of the absolute values of the charges and inversely proportional to the square of the distance between them. This law provides the mathematical foundation to calculate forces when charges are placed in space.

Superposition Principle

The superposition principle in electrostatics states that the net force acting on a charge is the vector sum of the individual forces exerted by each of the other charges. This means that when multiple charges are present, each exerts its own force independently, and these forces can be added together to find the total force acting on any given charge.

Transcript

00:01 And this problem, you have two charges, q1 and q2, call this guy 1 and this guy 2.

00:12 You're told that they are 0 .6 meters apart from each other.

00:19 And you're asked to find a location near them where when i place a small test charge positive q, the force on that test charge is going to be zero.

00:27 Now, you're told in the problem, this guy is a positive charge, and this guy is negative.

00:31 In fact, we know that q1 is equal to 2 .5 microcholums and q2 is 3 .5 microcolons, but negative microcolums.

00:50 And so the q2 is larger in magnitude.

00:54 So can this position exist in between them? well, if i put it here, the positive charge is going to repel a positive.

01:02 The negative is going to attract it, so no, it can't be there.

01:04 If i put it out here on the left, sorry, on the right -hand side, the negative charge is going to overwhelm whatever the positive can do, so it cannot exist over here.

01:15 So the location is going to have to be on this side where i put my positive small test charge q.

01:22 So that's where that's going to have to exist.

01:27 So if i, and it tells me the problem that q1 is at location zero, x equals zero.

01:33 So this positive charge is going to exist a distance x from q1.

01:40 And of course, that means it's x plus 0 .6 from q2.

01:45 The premise of this problem is you're going to use koololum's law, f equals k, q1, q2 over r squared, to solve this problem.

01:56 So let's go ahead and do it and see what we get.

02:00 So i'm going to have two forces acting.

02:02 The force from charge 1 plus the force from charge 2 has got equals 0.

02:08 F1 is going to be k -q1 -q over r squared, and the force from 2 is going to be k -q -2 -q over r -squared.

02:24 That all has to equal zero.

02:27 I've got to be careful here because this is r1 and this is r2.