Dipole - the calc. seems a bit illogical though correct

[exuberant.me]

I was reading the calculation for calculating the electric field due to a dipole at any point P at a distance x from the center of the dipole.

the way they have written the calc. seems a bit illogical

they have broken p into two components pcosθ and psinθ and applied E = kp/r³

Now,


E = Ex + Ey = (kpcosθ)/r³i + (kpsinθ)/r³j

but that would give the net field along some other direction..

it should rather only be

E = Ex = (kpcosθ)/r³

If someone can explain..!
Thanks in advance

 

[mfb]

Why? The electric field has both an x- and a y-component.

 

[exuberant.me]

i got it cleared at last... actually there was a different problem i faced.. but could not express it here...
btw.. i got it cleared by looking carefully..
they have done the right thing.. for first one it lies on the axial line and for second component it lies on equitorial plane.. i could not focus on this thing... thanks a lot.. !