The electric potential at a distance z from an electrically charged disk of radius R was given as

where k₁ is a constant.

(a) Suppose z is much larger than R. By writing

as

and using the Taylor polynomial of degree 1 for √1 + x, show that the potential can be approximated by

the result given in the Extended Application, where k₂ is a constant.

(b) Suppose z is much smaller than R. By writingas 

and using the Taylor polynomial of degree 1 for √1 + x, show that the potential can be approximated by

the result given in the Extended Application.

V = k( + R z),