Calculating Forces on a Corner with Identical Charges

[sayuri2009]

Homework Statement

Three identical charges +Q are placed at the vertices of an equilateral triangle of side a.
Evaluate the magnitude of the Coulomb force acting on each charge

Relevant Equations

Fc = kc * q^2 / r^2 (Coulomb force)

Hi everybody,

I tried to solve this problem but somehow I don't get it really. What I have to do. What I also know in this context is if its the same charge it will not attract otherwise if its the opposite charge it will attract. How do I have to calculate each charge on the corner?

Question is the following

What I already know is the following one:

I also know that the charges are repelling because they have the same charge.

Here is my calculation

So it means Fc = kc * (q^2 + q^2 + q^2) / a^2 = kc * 3q^2 / a^2 but the correct solution is C. Why? Where does the square root come from?

Thanks!

 

[BvU]

Hello @sayuri2009 , !

to solve this problem

I don't see a problem. Please state the problem text exactly as it was given to you. What is given, what is to be calculated ?

Also, read the https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

It tells you that you get no assistance in PF unless you post your own attempt at solution !

 

[sayuri2009]

Thanks BvU I changed it and tried to follow!

 

[BvU]

Good (my post hangs in the air now, never mind). Apart from that, this thread is sound now.

Evaluate the magnitude of the Coulomb force acting on each charge
Relevant Equations:: Fc = kc * q^2 / r^2 (Coulomb force)

So it means Fc = kc * (q^2 + q^2 + q^2) / a^2 = kc * 3q^2 / a^2

If I try to follow your work, you add three force magnitudes. Can you point them out in your picture ?

 

[hutchphd]

The forces are vector quantities. You must add them as vectors. Do you know how to do that?

 

[sayuri2009]

Good (my post hangs in the air now, never mind). Apart from that, this thread is sound now.

If I try to follow your work, you add three force magnitudes. Can you point them out in your picture ?

I don't what do you mean to point out those forces.

 

[sayuri2009]

The forces are vector quantities. You must add them as vectors. Do you know how to do that?

Thanks, for your reply. Hmm which one should I add? Didn't I already add those charges?

 

[BvU]

I don't what do you mean to point out those forces.

There are six arrows in your sketch. How big are they each individually ?
And how do you add them ?

 

[sayuri2009]

There are six arrows in your sketch. How big are they each individually ?
And how do you add them ?

Because they have the same charge I just add each charge -> Q + Q + Q = 3 Q

 

[hutchphd]

No that is incorrect. Force is a vector. It has magnitude and direction. That is why you draw them as arrows. Surely you have covered this in class? It is fundamental to physics and engineering.

 

[sayuri2009]

No that is incorrect. Force is a vector. It has magnitude and direction. That is why you draw them as arrows. Surely you have covered this in class? It is fundamental to physics and engineering.

Yes we had that long time ago. But how do I have to calculate the charges? I am bit confused now.

 

[hutchphd]

You need to review vector addition. You did not learn it well enough.

 

[BvU]

Let me try again:

What is the magnitude of the force that the charge on the lower left exerts on the charge at the top ?

 

[sayuri2009]

The magnitude will be Q? Now I tried to

Let me try again:
View attachment 275558
What is the magnitude of the force that the charge on the lower left exerts on the charge at the top ?

Now I tried to draw the forces into the triangle. The magnitude on the lower left will q or not?

 

[BvU]

The magnitude on the lower left will q or not?

I am afraid I do not understand that question.

Did you also not understand my question ? You did not answer it...

 

[Steve4Physics]

[EDIT: This is a question for @sayuri2009]

Can I chip in? Can you answer these 2 questions?

1) Two forces, each 20N north, act on an object. What is the magnitude and direction of the resultant force on the object?

2) Two forces act on an object. One force is 20N acting 30º east of north. The other force is 20N acting 30º west of north. What is the magnitude and direction of the resultant force on the object?

Unless you understand/know how to answer these questions, you won't be able to answer the question about the forces acting on the charges.

 

[Delta2]

If you have two forces of magnitude $F_1,F_2$ respectively and these two forces make an angle $\phi$ then their resultant force has magnitude $F$ ,$$F=\sqrt{F_1^2+F_2^2+2F_1F_2\cos\phi}$$.

How can you apply this knowledge to your problem? What $F_1,F_2$ and $\phi$ are equal to , in your specific problem?

If you are interested how do we get the above formula you should read about Law of Cosines.
Law of cosines - Wikipedia

 

[jbriggs444]

Now I tried to draw the forces into the triangle. The magnitude on the lower left will q or not?

The letter "q" is usually used to denote charge. That is how it is used in this problem. It is not used to denote a force.

The force that exists between two [point] charges is given by Coulomb's law:$$F=k\frac{q_1 q_2}{r^2}$$where $F$ is the force, $k$ is Coulomb's constant, $q_1$ and $q_2$ are the values of the two charges and $r$ is the distance between them.

 

[sayuri2009]

I am afraid I do not understand that question.

Did you also not understand my question ? You did not answer it...

Sorry not really I do not understand. What should I do...

 

[sayuri2009]

[EDIT: This is a question for @sayuri2009]

Can I chip in? Can you answer these 2 questions?

1) Two forces, each 20N north, act on an object. What is the magnitude and direction of the resultant force on the object?

2) Two forces act on an object. One force is 20N acting 30º east of north. The other force is 20N acting 30º west of north. What is the magnitude and direction of the resultant force on the object?

Unless you understand/know how to answer these questions, you won't be able to answer the question about the forces acting on the charges.

I think it should be like this?
1) Both forces are showing in the same direction and together it makes 40 N?
2) R^2 = 20^2 + 20^2 -2 * 20 * 20 * cos(50)?

 

[Steve4Physics]

I think it should be like this?
1) Both forces are showing in the same direction and together it makes 40 N?
2) R^2 = 20^2 + 20^2 -2 * 20 * 20 * cos(50)?

1) 40N is correct but I asked for the direction too. You haven't given it.
2) Where does the '50' come from (it's wrong)? You haven't worked out R. You haven't given the direction.

Call the 3 charges A, B and C. Suppose you want the total force (size and direction) on charge A.

There are 2 forces on A:
A is repelled by B; this force on A acts in the direction BA;
A is repelled by C; this force on A acts in the direction CA.
You have to work out each force (they have the same magnitude) using your formula (post#1).
Then you have to add these 2 forces allowing for their different directions, as in my question 2) (above).

There are several ways to add forces (vectors). You need to go back to your notes/text-book, and maybe watch a few YouTube videos. Unless you first learn how to add vectors, in different directions, we can't guide you through the original problem with the charges.

 

[sayuri2009]

1) 40N is correct but I asked for the direction too. You haven't given it.
2) Where does the '50' come from (it's wrong)? You haven't worked out R. You haven't given the direction.

Call the 3 charges A, B and C. Suppose you want the total force (size and direction) on charge A.

There are 2 forces on A:
A is repelled by B; this force on A acts in the direction BA;
A is repelled by C; this force on A acts in the direction CA.
You have to work out each force (they have the same magnitude) using your formula (post#1).
Then you have to add these 2 forces allowing for their different directions, as in my question 2) (above).

There are several ways to add forces (vectors). You need to go back to your notes/text-book, and maybe watch a few YouTube videos. Unless you first learn how to add vectors, in different directions, we can't guide you through the original problem with the charges.

1) Direction the are going to the north?
2) Sorry, its cos(30) I overlooked the value. Should I do the whole calculation of it?

Ok I have revise the forces and vectors addtion again and I will come back in few days!

 

[Steve4Physics]

1) Direction the are going to the north?
2) Sorry, its cos(30) I overlooked the value. Should I do the whole calculation of it?

Ok I have revise the forces and vectors addtion again and I will come back in few days!

1) Yes, to the north.
2) It is not 30 degrees. Have you drawn a diagram showing the two forces you are adding? You should try to complete this problem. You need to fully understand how to do it in order to answer the original question about the charges.

 

[sayuri2009]

1) Yes, to the north.
2) It is not 30 degrees. Have you drawn a diagram showing the two forces you are adding? You should try to complete this problem. You need to fully understand how to do it in order to answer the original question about the charges.

2) Before I didn't draw it. But now I did draw it. its cos(60)? Because 20N acting 30º east of north and the other force is 20N acting 30º west of north

 

[Steve4Physics]

2) Before I didn't draw it. But now I did draw it. its cos(60)? Because 20N acting 30º east of north and the other force is 20N acting 30º west of north

It is not 60 either! But you are getting closer! It looks like you haven't revised vector addition, so you are simply guessing.

And you still haven't said what direction the resultant is.

Look at this image:
https://www.misumi-techcentral.com/tt/en/lca/486_3.gif

The 2 black forces are being added. The total (resultant) is the brown force. To add the forces you can use either :
a) the parallelogram method (left diagram) or
b) a force addition triangle (right diagram).

What is the angle between the 2 black lines in a)?
What is the angle between the 2 black lines in b)?

If you want to use the cosine rule, you use the triangle (b), right hand diagram). Make sure you understand how the cosine rule works and what the correct angle is.