**how much work must be done to pull the plates apart to where the distance between them is 2.0 mm?** This is a topic that many people are looking for. **bluevelvetrestaurant.com** is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, ** bluevelvetrestaurant.com ** would like to introduce to you **Physics – E&M: Ch 35.1 Coulumbs Law Explained (26 of 28) Charges Suspended on a String: Ex. 1**. Following along are instructions in the video below:

To electron line. Here we have two objects that contain charge q. And have mass mass m.

Theyre both suspended from a string. Now if there is no charges. The two objects that would be sitting side by side.

But because the repulsive force they are repelling each other theyre pushed to the side. And so the strings. Now make an angle of theta relative to the vertical.

The length of each string is equal to l. And the question is based upon the angle. The length l.

The mass m and the charge q. What is q equal to in terms of all these other components well to do that what you need to do is draw some vectors representing the forces acting on these two spheres first of all theres a force of repulsion due to the coulomb forces. Which means.

This charge is going to be pushed to the right with a force f sub c. And thats going to be equal to k times q times q. Divided by the distance between them squared on the other side.

You have a similar force pushing discharge to the left and again. The coulomb force is going to be equal to k. Times.

The product of the two charges divided by the distance between them squared next. We realize that since i have mass. There also being attracted towards the earth due to gravity.

So i have a force pulling downward. So this is going to be m times g. And its the same for this force right here for this side.

Its going to be a force equal to m times g. And then if we take a look at each one of those charges. Separately.

We realize that theres a force pull in this case. A force pushing to the right a force pulling to the left and then theres a tension in the string pulling of the object this way and since everything is now in static equilibrium. And not we dont mean charge.

Why static. We simply mean that nothing is moving all the forces should add up to zero. Which means we could take these three forces and add them together victory and that should add up to zero.

Which means we can draw them in a triangular format. So we have the force due to the tension that looks like this we have the force gee pulling downward and then we have the coulomb force pulling the object to the right so this would be f sub c. And then this would then be the angle theta now all three forces add together should add up to zero.

Which means we can now find the relationship between these two forces. We can now claim that the tangent of the angle. Theta is going to be equal to the opposite side divided by the adjacent side and notice that in this case.

The opposite side would be the coulomb force f sub c. And the adjacent side would be the weight of the objects m g. And thats going to be our starting point to try to find out what the value of q is in terms of everything else.

So lets again write the equation that the tangent of theta is equal to the coulomb force divided by the weight of the object. So we can write that the tangent of theta is equal to the coulomb force. Can then be written as k.

Times. Q. Squared over the distance between them all right.

So the distance between these two charges. Lets say well that would be this distance right here d. And if were bring this all the way down.

Then we could say that this distance right here would be distance over two and well well get there in just a moment. Well write down. What we need to write down.

So 1 2 k. Q. Squared divided by the distance between them squared and that would divide that by m g.

So solving this for q. Squared. We have q.

Squared is equal to d. Squared. Mg.

Tangent of theta all divided by k. Lets see. If thats correct here.

So we have d. Squared mg. Comes over here put them together divided by k.

Yes. Now we then say that q is equal to d times. The square root of mg times.

The tangent of theta divided by k of course k is nine times in the ninth newtons meter. Squared per coulomb squared. The only thing left to do is find d in terms of everything else.

So. What we can say here based upon this triangle is that d divided by two is equal to the hypotenuse l. Times.

The sine of the angle theta because d over two is opposite of the angle. So we take the hypotenuse l. Times.

The sine of the angle. Theta should equal the opposite side d over 2. Which means that d is equal to 2l sine theta.

Then we come back over here we plug that in here so q is equal to d. Which is 2l sine theta times the square root of mg tangent of theta divided by k. And if you given any values for any of these if youre given the length the angle.

The mass of it and well thats it you need the length the angle and the mass of the object you can then find the charge on each of the two two objects. And thats how its done. .

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