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## Homework Statement

Charges +/- q separated by a distance d make a dipole with dipole moment qd. For large r the potential approaches qdcosθ/(4πε

_{0}r²). For θ=0, how large must r be so that the asymptotic function is accurate to 1%?

## Homework Equations

Exact V= q

_{1}/(4πε

_{0}r) + q

_{2}/(4πε

_{0}r)

Approximate V= qdcosθ/(4πε

_{0}r²)

## The Attempt at a Solution

I understand that the following statement must be true:

Vexact - Vapproximate ≤ 1.0%(Vexact)

q

_{1}/(4πε

_{0}r) + q

_{2}/(4πε

_{0}(r-d)) - qdcosθ/(4πε

_{0}r²) ≤ 1.0 %.

If we cancel all like constants;

1/r - 1/(r-d) - d/r²) ≤ 1.0 %

I do not understand where to go from here, or even if my approach towards this is correct.

Thank you in advance to all those who are reading.