Moderate# The Field Parallel and Perpendicular to the Dipole Axis

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Figure 1 depicts an electric dipole, in which the separation between the positive and negative charges is equal to $\alpha = 3.9 \text{ pm}$, and the magnitude of each charge is equal to $q = 10e$, where $e = 1.602 \times 10^{-19} \text{ C}$ is the electronic charge.

The point $P_\parallel$ is a distance $z$ from the center of the dipole along the $\hat{y}$ axis, and the point $P_\perp$ is a distance $x$ from the center of the dipole axis along the $\hat{x}$ axis.

What is the ratio of the magnitude of the electric field perpendicular to the dipole axis to the magnitude of the electric field along the dipole axis, $R = \cfrac{E(P_\parallel)}{E(P_\perp)}$ at the points $P_\parallel$ and $P_\perp$ such that $x = z = 4.3 \text{ nm}$?