Answer
(a) $E' = 250~N/C$
(b) $E' = 4000~N/C$
Work Step by Step
We can write an expression for the strength of the electric field which is 1000 N/C:
$E = \frac{kq}{d^2}$
(a) We can find the field strength when the distance is doubled.
$E' = \frac{kq}{(2d)^2}$
$E' = \frac{1}{4}~\frac{kq}{d^2}$
$E' = \frac{E}{4}$
$E' = \frac{1000~N/C}{4}$
$E' = 250~N/C$
(b) We can find the field strength when the distance is halved.
$E' = \frac{kq}{(d/2)^2}$
$E' = 4~\frac{kq}{d^2}$
$E' = 4E$
$E' = (4)(1000~N/C)$
$E' = 4000~N/C$
