Solving Force of Charges Problem - 1nC Charge in Middle

[cemar.]

Homework Statement

What is the force F on the 1nC charge in the middle due to the four other harges? Give your answer in component form.

There is a picture that i don't know how to get up so ill just describe it.

There are four charges in a square, length of square = 1cm. the two charges on the left corners of the square are -2nC and the two charges on the right corners of the square are +2nC. There is a charge in the middle of the square of +1 nC.

Homework Equations

I'm just using F= (kq1q2/r^2)

The Attempt at a Solution

so what I am doing is a force diagram and from that i know that the y components cancel out. the magnitude of the forces is equal, therefore their x components will be equal. Using the force equation under step two i determined the magnitude of the force and from that was able to determine the x component with cosine and a 45 degree angle. I then multiplied the x component by 4.
The answer i ended up with was 5.1E-4 where the real answer is actually double that.

Thanks!

 

[Shooting Star]

The concept is correct. There must have been some arithmetical mistake somewhere. Show your calculations briefly.

 

[Moetasim]

I would like to commend you on your approach to solving this problem. It is important to start with a force diagram and use the correct equation (Coulomb's Law in this case) to determine the magnitude and direction of the force. Additionally, taking into account the symmetry of the charges and using trigonometry to determine the components is a valid method.

However, it seems that you may have made a small error in your calculations. When determining the x component of the force, the angle should be 45 degrees (not cosine of 45 degrees) and you should only multiply by 2, not 4. This would result in a final answer of 1.02E-3, which is double the value you obtained.

Overall, your approach is sound and with some minor adjustments, you were able to obtain the correct answer. Keep up the good work!