Point chages q and -q are located at the verticles of a squre with diagonals 2l as shown in fig. Evaluate the magnitude of the electric field strength at a point located symmetrically with respect to the vertices of the square at a distanc x from the center.

Answer

`|vec(E )|=(ql)/(sqrt(2)pi epsilon_(0)(x^(2)+l^(2))^(3//2))`

Explanation

`E_(1)=2Ecos theta =(2kq(l))/([x^(2)+l^(2)]^(3//2))` along AC
`E_(2)=2Ecos theta =(2kql)/([x^(2)+l^(2)]^(3//2))` along DB
So `E_(1)_|_E_(2)` Net field is
`E_(0)=sqrt(E_(1)^(2)+E_(2)^(2))=(2sqrt(2)kql)/((x^(2)+l^(2))^(3//2))=(ql)/(sqrt(2)pi epsilon_(0)(x^(2)+l^(2))^(3//2))`