Along the axis of a small charged sphere embedded in a dielectric medium

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Along the axis of a small charged sphere embedded in a dielectric medium, the magnitude

E

(in newtons per coulomb) of the electric field at a distance

r

meters from the sphere’s center is modeled for

r>0.02

E(r)=\frac{kQ}{(r-0.02)^2}+5,

where

k

and

Q

are positive constants. (a) Calculate

\displaystyle \lim_{r\to 0.02^{+}}E(r)

and describe what this result signifies about the field strength near the surface of the sphere. (b) Determine

\displaystyle \lim_{r\to\infty}E(r)

and interpret the physical meaning of this limit. (c) Identify all vertical and horizontal asymptotes of

E

and explain how each asymptote relates to measurable behavior of the electric field.