Calculate the y component of the electric field at a generic point(x,y)

[blueyellow]

Homework Statement

an electric dipole is placed in the x-y plane, with the positive charge +q placed in position (+a, 0) and the negative charge -q placed in position (-a, 0)

define r(subscript +) and r(subscript -) the vectors connecting the point defined by r and the two points (+a, 0) and (-a, 0), and r(subscript+) and r(subscript -) their magnitudes; calculate the y component of the electric field at a generic point (x, y) of the plane as a function of r(subscript +) and r(subscript -) (it is quicker to use directly the field equation from a point charge than using the potential)

The Attempt at a Solution

E=-gradV=q/(4 pi epsilon0)(1/(r^2)) r-hat

E=q/(4pi epsilon0) [(1/([r(+)]^2 +(x+a)^2))+(1/([r(-)]^2 + (x-a)^2))]

 

[Spinnor]

In the above was a hint:

"... (it is quicker to use directly the field equation from a point charge than using the potential) ... "

The first line of your solution you have E=-gradV ...

I think you are to just add two electric vectors?

 

[blueyellow]

sorry, I still don't understand. where have I gone wrong?