Two equal and opposite point charges form a dipole, as shown in Fig. 15.29.

(a) Add the electric fields due to each end at point P, thus graphically determining the direction of the field there.
(b) Derive a symbolic expression for the magnitude of the electric field at point P, in terms of k, q, d, and x.
(c) If point P is very far away, use the exact result to show that E ‰ˆ kgd/x3.
(d) Why is it an inverse-cube falloff instead of inverse-square? Explain why it is not an inverse square falloff.

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