Acertain electric dipole consists of charges q and –q separated by distance d, oriented along the x-axis as shown in the figure. find an expression for the magnitude of the electric field e of the dipole at a point far away in the y-direction, a distance r away from the midpoint of the dipole. assume that r is much greater than
d. enter your answer in terms of q, d, r, and ε0.

We use the formula
E = Q / 4πε₀R²
where Q is the charge
R is the distance between the point and the charge

Since there are two charges, we add them to get the total electric field.
The distance between the point and the charge is
R = √( (d/2)² + r²)
The resulting electric field is
Etotal = q / 4πε₀( (d/2)² + r²) + (-q / 4πε₀( (d/2)² + r²))
Which would equate to 0.
The net electric field is 0 since the charges are opposite and the point is located along the midpoint of the line that connects the two charges.