# Homework Help: Another Charge question

1. Aug 26, 2007

### Winzer

1. The problem statement, all variables and given/known data
The charges Q1= 1.90·10-6 C and Q2= -3.03·10-6 C are fixed at their positions, distance 0.279 m apart, and the charge Q3= 3.33·10-6 C is moved along the straight line. For what position of Q3 relative to Q1 is the net force on Q3 due to Q1 and Q2 zero? Use the plus sign for Q3 to the right of Q1.

2. Relevant equations
$$F=\frac{KQq_{1}q_{2}}{r^2}$$

3. The attempt at a solution
I get 0.6483m

2. Aug 26, 2007

### Staff: Mentor

Please give the coordinate of each particle along an axis.

3. Aug 26, 2007

### rootX

4. Aug 26, 2007

### Winzer

Q(0,0), Q2(.279,0), Q3(x,0). Where X>.279m

5. Aug 26, 2007

### Staff: Mentor

That's what I thought you were saying. Note that X > .279 is not a requirement of the problem, but something that you added. In fact, it can't be true!

6. Aug 26, 2007

### Winzer

True, i did add that in.
I started by finding the force between q1 and q2:
$$F=\frac{9.0e^9 1.90e^-6 -3.03e^-6}{.279^2}=-6.65e^-1N$$
Then I can set that equal to $$F=\frac{KQq_{1}q_{2}}{(x-r)^2}$$, right?

7. Aug 26, 2007

### rootX

just making it way too complex,
find where E is 0, and that would be the position of Q3
and you would get something like
q/r^2 = q1/(d+r)^2

8. Aug 26, 2007

### Staff: Mentor

The force between Q1 and Q2 is irrelevant. You want the force on Q3! (Hint: Where does the electric field of Q1 + Q2 equal zero?)

The first thing I would do is figure out which region Q3 must be in:
(a) to the left of Q1
(b) between Q1 and Q2
(c) to the right of Q2

Last edited: Aug 26, 2007
9. Aug 26, 2007

### Winzer

So: $$E_{1}+E_{2}=0$$
$$\frac{kq_{1}}{x^2}-\frac{kq_{2}}{(r+x)^2}=0$$

10. Aug 26, 2007

### Staff: Mentor

What region are you analyzing? What's the definition of x?

If it's not obvious which region Q3 must be in, study each region systematically.

11. Aug 26, 2007

### Winzer

the region right of q2. X is distance from q1 to q3

12. Aug 26, 2007

### Staff: Mentor

For some reason you are choosing the region to the right of q2 (even though I told you that it was impossible! ). No problem! If x is the distance from q1, what must be the distance from q2 in that region?

13. Aug 26, 2007

### Winzer

ok, so I the region where E=0, q3 would have to inbetween q1 & q2. getting confused

14. Aug 26, 2007

### Staff: Mentor

Don't give up on studying any region. If you pick the wrong region, the equation you get will not give you an answer in the region.

To study the region in between q1 & q2, draw yourself a picture. In that region, which way would the field from q1 point? The field from q2? Could they cancel?

15. Aug 26, 2007

### Winzer

I know the q1 field is outward and q2 field in inward. So the field(right side) from q1 to q2 will interect with each other.

16. Aug 26, 2007

### Staff: Mentor

Right! So, in the region between q1 and q2, which way does each field point: to the right or to the left? If we let positive stand for "to the right", are the fields positive or negative in that region?

17. Aug 26, 2007

### Winzer

positve to the right, negitive to the left

18. Aug 26, 2007

### Staff: Mentor

That's the sign convention. But which way do the fields point?

19. Aug 26, 2007

### Winzer

The combination of the q1 and q2 field points to the right.

20. Aug 26, 2007

### Staff: Mentor

In that middle region, the field from q1 points to the right (and thus is positive) and the field from q2 also points to the right (and is positive). So is it possible for the fields to cancel out in that region?

21. Aug 26, 2007

### Winzer

mmm..yes

22. Aug 26, 2007

### Staff: Mentor

Answer this: If A is positive and B is positive, can A+B ever equal zero?

23. Aug 26, 2007

### Winzer

If both A and B are positive than there is an efield that is zero at some point. Because both field lines from A and B will repel each other.

24. Aug 26, 2007

### Staff: Mentor

No. If A and B are positive, their sum must also be positive. They can never add to zero. You can only get 2 numbers to sum to zero if they have different signs.
The fields from each charge (q1 & q2) point in the same direction and thus add together--they don't cancel. That tells you that the force on q3 will never be zero if it's placed between q1 and q2. (Now you need to check the other two regions.)

25. Aug 26, 2007

### Winzer

so I suspect that the only way the fields repel if we put it before q1?