at what distance does the least accurate approximation for t

at what distance does the least accurate approximation for the electric field give a result that is closest to hte most accurate?

Solution

In electrostatics we deal with electric charges, and the elctric field always follow the law of summation. That means, Electric field caused by a charge distribution is equal to the sum of the electric fields caused by the individual point charges that constitute the charge distribution. Configuration of the charge distribution plays a crutial role to determine the electric field when it is measured from a distance comparable with the dimention of the charge configuration. But when electric field is measured from very large distance, then, only the total charge is what matters. In this case, one can approximate the charge configuratoin as a point charge whose magnitude is equal to the total charge of the charge configutaion, and this is the least accurate approximation, which works nicely.

so the correct answer is : a distance which is far far larger than any length scale of the charge distribution.