Answer to Question #296819 in Electricity and Magnetism for lylou

Question

​(I) Four point charges are located at the vertices of a square with side L.

We give q2 ​= q3 ​= Q and q1​= q4 ​= −2Q.

​Determine the resulting electric field​ (a) at point A​,

in the center of the square; (b) at point B

Answer 1

$\vec E=\vec E_1+\vec E_2+\vec E_3+\vec E_4,$

a)

$E=2\sqrt 2\frac {kq}{L^2},$

b)

$E_x=\frac{8kq}{5\sqrt 5 L^2},$

$E_y=\frac{4kq(5\sqrt 5 -3)}{5\sqrt 5 L^2},$

$E=\sqrt{E_x^2+E_y^2}=\frac{4kq(138-30\sqrt 5)}{5\sqrt 5L^2}.$