Charges +/- q separated by a distance d make a dipole with dipole moment qd. For large r the potential approaches qdcosθ/(4πε0r²). For θ=0, how large must r be so that the asymptotic function is accurate to 1%?
Exact V= q1/(4πε0r) + q2 /(4πε0r)
Approximate V= qdcosθ/(4πε0r²)
The Attempt at a Solution
I understand that the following statement must be true:
Vexact - Vapproximate ≤ 1.0%(Vexact)
q1/(4πε0r) + q2 /(4πε0(r-d)) - qdcosθ/(4πε0r²) ≤ 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.