A charge distribution generates a radial electrif field `vecE=(a)/(r^(2))e^(-(r)/(k))hatr`, where r is distance from the origin `hatr` is a unit vector in radial direction away from the origini and a and k are positive constants. The electric field extends around the origin up to a large distance.
(a). Find the charge `(q_(0))` that must be located at the origin to create such a field
(b). Find the quantity of charge (q) that must be spread around the charge `q_(0)` at origin to create such a field.

Answer

(a). `q_(0)=4pi epsilon_(0)a`
(b). `q=-4pi epsilon_(0)a`