# Finding the accuracy of an approximated potential

1. Feb 4, 2015

### Electroguru

1. The problem statement, all variables and given/known data
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%?

2. Relevant equations
Exact V= q1/(4πε0r) + q2 /(4πε0r)
Approximate V= qdcosθ/(4πε0r²)

3. 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.

2. Feb 4, 2015

### Staff: Mentor

I think they meant for you to have the two charges at +d/2 and -d/2. When you get the two fractions, you should reduce them to a common denominator. Then, you might get an idea what to do next.

Chet