# Electrostatic field at the square center

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1. Mar 10, 2015

### tom75

I have just begun studying electrostatic and I'm trying to do this exercize:

We have a square with charges +q , -2q, +2q, -q

1)Compute the electrostatic field $$\vec{E}$$at the center of the square.

I did this way :

I find $$\vec{E_A}=\frac{q}{2 \pi \epsilon_0} \vec{u}$$
$${E_B}=\frac{-q}{ \pi \epsilon_0} \vec{u}$$
$${E_C}=\frac{q}{ \pi \epsilon_0} \vec{u}$$
$${E_D}=\frac{-q}{2 \pi \epsilon_0} \vec{u}$$

Then with projection :

$$E_A=\frac{q}{2 \pi \epsilon_0}*cos(45)=\frac{\sqrt{2}q}{4\pi \epsilon_0}$$

$$E_B=\frac{-q}{ \pi \epsilon_0}*cos(45)=\frac{-\sqrt{2}q}{2\pi \epsilon_0}$$

$$E_C=\frac{q}{2 \pi \epsilon_0}*sin(-45)=\frac{-\sqrt{2}q}{2\pi \epsilon_0}$$

$$E_D=\frac{-q}{2 \pi \epsilon_0}*sin(45)=\frac{-\sqrt{2}q}{4\pi \epsilon_0}$$

Finally $$E_{total}=\frac{-\sqrt{2}q}{\pi \epsilon_0}$$

Is-it correct ? I'm not sure of my way of reasoning and the projection.

Thank you

2. Mar 10, 2015

### rude man

You need to give the length of one of the sides; also the position of the four charges.

3. Mar 10, 2015

### tom75

Yes sorry the lenght of each side is 1 and this is a square with A (upper left), B(upper right) C(lower right) D(lower left) with respectively charges +q,-2q,+2q,-q

4. Mar 10, 2015

### rude man

What's the formula for the E field a distance d from a point source q?