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

1)Compute the electrostatic field [tex]\vec{E}[/tex]at the center of the square.

I did this way :

I find [tex]\vec{E_A}=\frac{q}{2 \pi \epsilon_0} \vec{u}[/tex]

[tex]{E_B}=\frac{-q}{ \pi \epsilon_0} \vec{u}[/tex]

[tex]{E_C}=\frac{q}{ \pi \epsilon_0} \vec{u}[/tex]

[tex]{E_D}=\frac{-q}{2 \pi \epsilon_0} \vec{u}[/tex]

Then with projection :

[tex]E_A=\frac{q}{2 \pi \epsilon_0}*cos(45)=\frac{\sqrt{2}q}{4\pi \epsilon_0}[/tex]

[tex]E_B=\frac{-q}{ \pi \epsilon_0}*cos(45)=\frac{-\sqrt{2}q}{2\pi \epsilon_0}[/tex]

[tex]E_C=\frac{q}{2 \pi \epsilon_0}*sin(-45)=\frac{-\sqrt{2}q}{2\pi \epsilon_0}[/tex]

[tex]E_D=\frac{-q}{2 \pi \epsilon_0}*sin(45)=\frac{-\sqrt{2}q}{4\pi \epsilon_0}[/tex]

Finally [tex]E_{total}=\frac{-\sqrt{2}q}{\pi \epsilon_0}[/tex]

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

Thank you