Two point charges q1 and q2 are held in place 4.50 cm apart. Another point charge Q=-1.75 μC, o

Two point charges q1 and q2 are held in place 4.50 cm...

Key Concepts

Coulomb's Law

Coulomb's Law quantifies the electric force between two point charges. It states that the magnitude of the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is fundamental in understanding how charges interact in an electrostatic field.

Principle of Superposition

The principle of superposition asserts that when multiple electric charges are present, the net electric force (or electric field) experienced by a charge is the vector sum of the forces (or fields) produced by each individual charge. This concept allows complex charge configurations to be analyzed by breaking them down into simpler components.

Electric Field and Force

The electric field is defined as the force per unit charge exerted on a small positive test charge placed in the vicinity of other charges. A charge within this field experiences an electric force, which can be calculated by multiplying the electric field by the magnitude of the charge. This concept connects the spatial distribution of charges with the forces they exert on one another.

Newton's Second Law

Newton's second law of motion states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In the context of electrostatics, this law is used to relate the force exerted by electric fields to the observed acceleration of charges, providing a bridge between electrical phenomena and kinematics.

Vector Analysis of Forces

In problems involving multiple forces, such as those arising from several point charges, vector analysis is essential. Each force has both magnitude and direction and must be resolved into components. The net result is obtained by summing these components vectorially, which is crucial for accurately predicting the motion of charges under the influence of electric fields.

Transcript

00:01 Hello everyone.

00:01 In this problem we're asked to find the magnitude of two point charges such that they have the following set up.

00:09 So they have we have point charge one with charge q1, point charge 2 with charge q2 and then we place a charge that is called big q that is a given distance away from both of these charges and we find that it has an acceleration that is away from both charges.

00:31 So this is midway between the two charges, and it's a distance of, let's see, so it's a distance of three centimeters from both.

00:46 It's three centimeters.

00:48 This is also three centimeters.

00:51 And the two -point charges q1 and q2 are a distance of 4 .5 centimeters away from each other.

01:01 Okay, so we see that the charge big q is going to accelerate and we're also told that the charge of that big charge is minus 1 .75 times 10 to the minus 6 couloms i .e.

01:19 Minus 1 .75 microculems.

01:22 Okay, so the question is what happens given that this charge, this big q charge has a mass of five grams so this five grams which is 5 .00 times 10 to minus three kilograms.

01:44 So this charge we noticed initially has an acceleration that is pointing up away from like parallel to the line that's bisecting the distance between q and q2 and it has a magnitude of three to fourths or 324 meters per second squared.

02:03 So this is a magnitude of three to fourths of three hundred and twenty four meters then the question is what is q1 and what is q2? okay, so this is what we're trying to find.

02:13 And so the way we're going to do this is that first we're going to have to find what the net force on this charge big q is.

02:23 So if we think about it, then if we draw a free -bellied diagram for this big q, one thing that we know we can kind of guess for sure is that these charges q1 and q2 are going to be negative because the charge that is negative, also bicu, is moving away from the objects.

02:46 So then let's assume that we have two coolant forces, fq1 on bik q and f q2 on bq that are acting on this object.

03:02 So what we're going to have to do now is resolve these forces.

03:07 So we're going to have to find what is the x and y components of these two fs.

03:14 So this is one, this is two, just to make sure that they are vectors.

03:19 And so if we know that the triangle that we're dealing with here is an isocelus triangle with sides 3, 3, and 4 .5, then we can figure out what the angle is.

03:36 So we know that this can be bisected such that this length over here is a half of 4 .5.

03:45 So that's half of 4 .5.

03:47 And then we can find out the angle down at the base over here.

03:54 I'm just using the cosine function.

03:58 So we have that data over there is equal to the inverse cosine of adjacent.

04:07 So 4 .5 over 2, 4 .5 over 2 divided by the hypotenuse, which is 3.

04:16 And so we get that that is cosine 4 .5 over 2 times 3.

04:26 So that is 41 degrees roughly.

04:30 So this is 41 degrees.

04:34 So what it tells us then is that this angle here is theta and this angle here is also theta.

04:44 So now that we have the angle, we can work out what the sum of the x components of the forces are.

04:51 So we have f net x acting on the charge is going to be equal to, let's take the right direction to be positive.

05:02 So i'm going to choose my xe such that this is the positive x direction this is the positive y direction and let's go so then we're going to have f1 or sorry f q1 on q x is the thing that's acting in a positive x direction and then we have f q2 on q x acting in the negative x direction so if we want to associate values to this then we're going to see that the first cool on force so this is to be, remember that the cool one force is just k times q1, q2, where these are the two charges that are interacting divided by the separation between them square.

05:49 So this is the magnitude of the coolant force.

05:54 And so if we use this cool on force, then we find that k times q1 q over r1 to q squared is the first force...

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