# Coulomb's law partII

1. Sep 11, 2007

### itzxmikee

Hi guys, these are the final 2 problems that Ive been struggling with for the past day. Please help

1. Four point charges are situated at the corners of a square with sides of length a, as in Figure P15.4.

Figure P15.4
Find the expression for the resultant force on the positive charge q.(Use k_e for ke, q for q, and a for a.)

2. Fe = ke(|q||q|/r^2)

3. So I found the x and y components of all the -q. But still get a big sloppy answer.

Question 2

An electron is released a short distance above the surface of the Earth. A second electron directly below it exerts an electrostatic force on the first electron just great enough to cancel the gravitational force on it. How far below the first electron is the second?

Im sure you have to use coulombs law again. But I just dont know where to start with this question.

Thanks guys

2. Sep 11, 2007

### Staff: Mentor

What did you get?

What forces act on the first electron? What's the net force on it?

3. Sep 11, 2007

### itzxmikee

The x components are
-ke(q^2/a^2) - ke(q^2/2a^2)cos45

and the y compents are
-ke(q^2/a^2) - ke(q^2/2a^2)sin45

after simplifications I get the magnitude to be:
sqrt(-2.7keq^2/a^2)

What forces act on the first electron? What's the net force on it?

The forces is weight? mass*gravity?
Net force? weight?

4. Sep 11, 2007

### lylos

It states that the electron below it exerts a force on it great enough to just cancel the force of gravity. So what do we know about the force of gravity and the force due to the electrons repelling each other?

5. Sep 11, 2007

### itzxmikee

The net force is zero

6. Sep 11, 2007

### lylos

Great, so when drawing a free body diagram of the electron, you can see that the forces act in two opposite directions, and they must be equal to each other. Using the formulas for the force due to the electron and the force due to gravity, you can then find how far below electron 1 the second electron must be.

7. Sep 11, 2007

### itzxmikee

Ke (q^2)/r^2 = G m^2/r^2

So are we assuming the electrons are the exact mass and charge?
Did I set up the equation right? How do I go about solving for r if I dont know q and m?

8. Sep 11, 2007

### lylos

Now, we're not dealing with the gravitational attraction between the two electrons, rather the electron being pulled to the earth and then being repelled from the other electron. One side of the equation is correct, the other is not. If you look in your book you should be able to find the charge on an electron and the mass of an electron.

9. Sep 11, 2007

### itzxmikee

Im assuming Ke (q^2)/r^2 is the correct side.
So would it be: Ke (q^2)/r^2 = Ke (q of electron)(q of earth)/r^2

10. Sep 11, 2007

### lylos

Alright, we have ke (q^2)/(r^2) on the left, and we need to set that equal to the mass of the electron * the acceleration due to gravity.

You sould then have:

Ke (q^2)/(r^2) = m (9.8)

You know Ke, q is the charge of the electron, which should be provided, m, is the mass of the electron, again which should be provided, the 9.8 is the acceleration due to gravity. Now you just solve for r.

11. Sep 11, 2007

### itzxmikee

duhh makes total sense now. Thank you Lylos!!!!!!

now with the 1st problem. Can anybody help me with that?

12. Sep 11, 2007

### lylos

What you need to do on the first problem is find the X and Y components of the force. Then add them together. For example, the force on q+ due to the q- directly above would be (kqq)/r^2 in the +y direction. Now the force due to the charge to the right would be (kqq)/r^2 in the +x direction. Now the hard part is trying to break down the force due to the charge in the upper right hand corner. It will have an independent x component and an independent y component. Once you have these values you can then find the resultant vector of force.

13. Sep 11, 2007

### Staff: Mentor

OK:
(1) Realize that $\sin (45) = \cos (45) = \sqrt{2}/2$
(2) Why negative?

I assume you mean: sqrt(2.7)keq^2/a^2

Recheck this; I get a different answer.

14. Sep 11, 2007

### itzxmikee

Okay just looked over the problem again

so I ended up with:

x components:
ke(q^2/a^2) + ke(q^2/2a^2)cos45
=(1+cos45(.5))(ke(q^2/a^2)
= 1.35(ke(q^2/a^2))

and the y components are:
ke(q^2/a^2) + ke(q^2/2a^2)sin45
=(1+sin45(.5))(ke(q^2/a^2)
= 1.35(ke(q^2/a^2))

So to find the magnitude:
((1.35(ke(q^2/a^2))^2 + (1.35(ke(q^2/a^2))^2) ^1/2

am I on the right track?

15. Sep 11, 2007

### Staff: Mentor

Yes, exactly. (Just be careful to square--and square root--things properly: you are missing a few parentheses.)

16. Sep 11, 2007

### itzxmikee

Thanks everyone. Until next time

17. Jan 25, 2008

### johnk1317

Hi I had a question considering this problem. The formula you generate is correct but I dont see how you got it. I will use x to represent the k*q^2/a^2

What I got:
(1+sin45)x for the y axis
(1+cos45)x for the x

What you got:
(1+sin45*.5)x
(1+cos45*.5)x

Where did you derive the .5 from? Thanks for the help.
John

18. Jan 26, 2008

### Staff: Mentor

Realize that the distance to the charge on the opposite corner is not a, but $\sqrt 2$a. That's where the .5 comes from.

19. Jan 26, 2008

### johnk1317

Thanks for the clarification
The text passage contains two distinct physics problems, both of which involve mathematical questions. The first problem is about finding the resultant force on a positive charge q placed at one corner of a square with point charges at each corner. The second problem is about determining the distance between two electrons where the electrostatic force between them cancels the gravitational force on one of the electrons.
multiple_questions

1. **first problem:**
   - **question:** find the expression for the resultant force on the positive charge q.
   - **answer:** the text provides a detailed discussion and partial solution, but it does not provide a final, complete answer.

2. **second problem:**
   - **question:** how far below the first electron is the second electron if the electrostatic force between them just cancels the gravitational force on the first electron?
   - **answer:** the text provides a detailed discussion and partial solution, but it does not provide a final, complete answer.

in both cases, the text provides a framework for solving the problems but does not give the final numerical or symbolic answers.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Coulomb's law partII

1. Sep 11, 2007

### itzxmikee

Hi guys, these are the final 2 problems that Ive been struggling with for the past day. Please help

1. Four point charges are situated at the corners of a square with sides of length a, as in Figure P15.4.

Figure P15.4
Find the expression for the resultant force on the positive charge q.(Use k_e for ke, q for q, and a for a.)

2. Fe = ke(|q||q|/r^2)

3. So I found the x and y components of all the -q. But still get a big sloppy answer.

Question 2

An electron is released a short distance above the surface of the Earth. A second electron directly below it exerts an electrostatic force on the first electron just great enough to cancel the gravitational force on it. How far below the first electron is the second?

Im sure you have to use coulombs law again. But I just dont know where to start with this question.

Thanks guys

2. Sep 11, 2007

### Staff: Mentor

What did you get?

What forces act on the first electron? What's the net force on it?

3. Sep 11, 2007

### itzxmikee

The x components are
-ke(q^2/a^2) - ke(q^2/2a^2)cos45

and the y compents are
-ke(q^2/a^2) - ke(q^2/2a^2)sin45

after simplifications I get the magnitude to be:
sqrt(-2.7keq^2/a^2)

What forces act on the first electron? What's the net force on it?

The forces is weight? mass*gravity?
Net force? weight?

4. Sep 11, 2007

### lylos

It states that the electron below it exerts a force on it great enough to just cancel the force of gravity. So what do we know about the force of gravity and the force due to the electrons repelling each other?

5. Sep 11, 2007

### itzxmikee

The net force is zero

6. Sep 11, 2007

### lylos

Great, so when drawing a free body diagram of the electron, you can see that the forces act in two opposite directions, and they must be equal to each other. Using the formulas for the force due to the electron and the force due to gravity, you can then find how far below electron 1 the second electron must be.

7. Sep 11, 2007

### itzxmikee

Ke (q^2)/r^2 = G m^2/r^2

So are we assuming the electrons are the exact mass and charge?
Did I set up the equation right? How do I go about solving for r if I dont know q and m?

8. Sep 11, 2007

### lylos

Now, we're not dealing with the gravitational attraction between the two electrons, rather the electron being pulled to the earth and then being repelled from the other electron. One side of the equation is correct, the other is not. If you look in your book you should be able to find the charge on an electron and the mass of an electron.

9. Sep 11, 2007

### itzxmikee

Im assuming Ke (q^2)/r^2 is the correct side.
So would it be: Ke (q^2)/r^2 = Ke (q of electron)(q of earth)/r^2

10. Sep 11, 2007

### lylos

Alright, we have ke (q^2)/(r^2) on the left, and we need to set that equal to the mass of the electron * the acceleration due to gravity.

You sould then have:

Ke (q^2)/(r^2) = m (9.8)

You know Ke, q is the charge of the electron, which should be provided, m, is the mass of the electron, again which should be provided, the 9.8 is the acceleration due to gravity. Now you just solve for r.

11. Sep 11, 2007

### itzxmikee

duhh makes total sense now. Thank you Lylos!!!!!!

now with the 1st problem. Can anybody help me with that?

12. Sep 11, 2007

### lylos

What you need to do on the first problem is find the X and Y components of the force. Then add them together. For example, the force on q+ due to the q- directly above would be (kqq)/r^2 in the +y direction. Now the force due to the charge to the right would be (kqq)/r^2 in the +x direction. Now the hard part is trying to break down the force due to the charge in the upper right hand corner. It will have an independent x component and an independent y component. Once you have these values you can then find the resultant vector of force.

13. Sep 11, 2007

### Staff: Mentor

OK:
(1) Realize that $\sin (45) = \cos (45) = \sqrt{2}/2$
(2) Why negative?

I assume you mean: sqrt(2.7)keq^2/a^2

Recheck this; I get a different answer.

14. Sep 11, 2007

### itzxmikee

Okay just looked over the problem again

so I ended up with:

x components:
ke(q^2/a^2) + ke(q^2/2a^2)cos45
=(1+cos45(.5))(ke(q^2/a^2)
= 1.35(ke(q^2/a^2))

and the y components are:
ke(q^2/a^2) + ke(q^2/2a^2)sin45
=(1+sin45(.5))(ke(q^2/a^2)
= 1.35(ke(q^2/a^2))

So to find the magnitude:
((1.35(ke(q^2/a^2))^2 + (1.35(ke(q^2/a^2))^2) ^1/2

am I on the right track?

15. Sep 11, 2007

### Staff: Mentor

Yes, exactly. (Just be careful to square--and square root--things properly: you are missing a few parentheses.)

16. Sep 11, 2007

### itzxmikee

Thanks everyone. Until next time

17. Jan 25, 2008

### johnk1317

Hi I had a question considering this problem. The formula you generate is correct but I dont see how you got it. I will use x to represent the k*q^2/a^2

What I got:
(1+sin45)x for the y axis
(1+cos45)x for the x

What you got:
(1+sin45*.5)x
(1+cos45*.5)x

Where did you derive the .5 from? Thanks for the help.
John

18. Jan 26, 2008

### Staff: Mentor

Realize that the distance to the charge on the opposite corner is not a, but $\sqrt 2$a. That's where the .5 comes from.

19. Jan 26, 2008

### johnk1317

Thanks for the clarification
user
The text passage contains two distinct physics problems, both of which involve mathematical questions. The first problem is about finding the resultant force on a positive charge q placed at one corner of a square with point charges at each corner. The second problem is about determining the distance between two electrons where the electrostatic force between them cancels the gravitational force on one of the electrons.

TYPE: MULTIPLE_QUESTIONS

1. **First Problem:**
   - **Question:** Find the expression for the resultant force on the positive charge q.
   - **Answer:** The text provides a detailed discussion and partial solution, but it does not provide a final, complete answer.

2. **Second Problem:**
   - **Question:** How far below the first electron is the second electron if the electrostatic force between them just cancels the gravitational force on the first electron?
   - **Answer:** The text provides a detailed discussion and partial solution, but it does not provide a final, complete answer.

In both cases, the text provides a framework for solving the problems but does not give the final numerical or symbolic answers.