## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

(a) $E' = 250~N/C$ (b) $E' = 4000~N/C$
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. $E' = \frac{kq}{(d/2)^2}$ $E' = 4~\frac{kq}{d^2}$ $E' = 4E$ $E' = (4)(1000~N/C)$ $E' = 4000~N/C$