# Finding The Effect of Several Electrics Fields

1. Feb 2, 2013

### Bashyboy

1. The problem statement, all variables and given/known data
Four charged particles are at the corners of a square of side a as shown in the figure below. (Let A = 5, B = 2, and C = 7.)

2. Relevant equations

3. The attempt at a solution
Well, I first found the electric due to each particle individually:

$\vec{E_A}=k_e\frac{5q}{a^2}\widehat{i}$

$\vec{E_B}=k_e \large[ \frac{2q~cos(45°)}{a^2}\widehat{i}+\frac{2q~sin(45°)}{a^2}\widehat{j}]$

$\vec{E_C}=k_e\frac{7q}{a^2}\widehat{j}$

Summing the effects of the each electric field together:

$\vec{E_{tot}}=k_e \large[(\frac{5q+2q\cos{45°}}{a^2}\widehat{i}+(\frac{2q \sin{45°}+7q}{a^2}\widehat{j}$

After simplifying, I found the magnitude of the electric field at point q, that the three particles create, to be $10.58 \cdot \frac{q}{a^2}$; however, the true answer is, $9.59 \cdot \frac{q}{a^2}$ What did I do wrong?

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Last edited: Feb 2, 2013
2. Feb 2, 2013

### Staff: Mentor

You did not include a diagram or describe what you are asked to find.

3. Feb 2, 2013

### Bashyboy

Sorry. I just attached one.

4. Feb 2, 2013

### Staff: Mentor

OK, what's the distance between B and q?

5. Feb 2, 2013

### Bashyboy

Wouldn't it be $\sqrt{2}a$?

6. Feb 2, 2013

### Bashyboy

I figured it would be better to resolve the electric field of B into its components.

7. Feb 2, 2013

### Staff: Mentor

Right.
Nothing wrong with that, but you must use the correct distance to calculate the field.

8. Feb 2, 2013

### Bashyboy

Well, to get from point B to point q, don't I have to go a units to right and a units north? What are the correct distances?

9. Feb 2, 2013

### Staff: Mentor

You just gave the correct distance in your earlier post. Use it!

10. Feb 2, 2013

### Bashyboy

Oh I see, I am mixing the idea of resolving charges and distances together.