# Yet another electric charge problem

1. May 13, 2007

### frankfjf

I got this problem wrong in my text's student companion website, but I don't understand why. Could someone let me know what went wrong?

1. The problem statement, all variables and given/known data

What are the horizontal and the vertical components of the resultant electrostatic force on the charge in the lower left corner of the square if q = 0.10 micro Coulombs (Or uC as I cannot remember how to type the Greek letter equivalent.) and a = 5.0cm?

2. Relevant equations

Fh = F-q + F-2q(cos(45))

Fv = -F+q + F-q(sin(45))

3. The attempt at a solution

I get .17E-6 N for Fh and -2.1E-7 N for Fv. I think I may have mixed up some decimal places on Fh, but the solution presented is .17 N for Fh and -0.046 for Fv. I just don't understand what I did wrong though.

2. May 13, 2007

### mbrmbrg

for Fh: your first term should be $$F_{-2q}$$, and your second term should be $$F_{-q}\cos(45^o)$$

for both: Please show more work. What is the general formula for the electrostatic force? What values did you use for each variable in the equation?

3. May 13, 2007

### frankfjf

My apologies. I'll try out your suggestion for Fh. Otherwise...

Fh = ((8.99E9)(2E-7)(1E-7)/.05^2) + (((8.99E9)(2E-7)^2)/.05^2)cos(45)

Fv = -((8.99E9)(2E-6)(1E-6)/.05^2) + ((8.99E9)(2E-6)(1E-6)/.05^2)sin(45)

4. May 13, 2007

### mbrmbrg

For Fv: as in Fh, the charges should be multiplied by 10-7

5. May 13, 2007

### frankfjf

After your suggestions I get .19E-8 for FH and -.02E-8. Why do my answers still differ from what the website presents? I don't get it.

6. May 13, 2007

### mbrmbrg

for the charge on the far corner: the distance is not 0.05m. It is along the diagonal of the square, not along one of the sides.
I'm checking now to see if that clears things up...

edit: I got the correct answer for both Fh and Fv when I took both of my suggestions (and the rest of your work ).

Last edited: May 13, 2007
7. May 13, 2007

### frankfjf

So for the charge in the far corner, it's not 0.05m? If not then how can I get the right measurement? The diagram doesn't give any indication of what the diagonal is. Or do you mean just the two suggestions you gave and the diagonal is a red herring so to speak?

8. May 13, 2007

### mbrmbrg

Cheese, frank, I wouldn't trick you like that!

You don't know the formula for the diagonal of a square? It's the same as the hypotenuse of a 45-45-90 triangle.

9. May 13, 2007

### frankfjf

Ah okay, that helped. Thanks!