What are the strength and direction of the electric field at the position indicated by the dot in the figure below, in which d = 5 cm and q = 5 nC? Specify the direction as an angle measured counterclockwise from the positive x-axis, which points to the right.
http://www.webassign.net/knight/p26-02.gif

Question

What are the strength and direction of the electric field at the position indicated by the dot in the figure below, in which d = 5 cm and q = 5 nC? Specify the direction as an angle measured counterclockwise from the positive x-axis, which points to the right. 
http://www.webassign.net/knight/p26-02.gif

michele_laino · Answer

we have to compute the vector sum between the electric fields exerted by each charge, as below:

michele_laino · Answer

as we can sse that sum has no component along x-direction

anonymous · Answer

$$Kq/(\sqrt{2}d)^2$$ this is the field due to a positive charge and negative charge individually. the direction of field ofr the positive will be towards it, however for the negative charge will be away from it. Hence, by geometry, we can say that the angle between theese two firld will be 90degrees. 
Hence, the net electric field becomes 
$$(1/2)*(Kq/(\sqrt{2}d)^2)* (\cos (\pi/2)/2)$$