Answer
The magnitude of the electric field is $3.3\times 10^6~N/C$ and it is directed downward.
Work Step by Step
We can find the sphere's weight.
$weight = mg$
$weight = (0.0010~kg)(9.80~m/s^2)$
$weight = 9.8\times 10^{-3}~N$
The magnitude of the electric force must be equal to the sphere's weight. We can find the magnitude of the electric field.
$F = E~q$
$E = \frac{F}{q}$
$E = \frac{9.8\times 10^{-3}~N}{3.0\times 10^{-9}~C}$
$E = 3.3\times 10^6~N/C$
Since the charge on the sphere is negative, the electric force on the sphere will be directed upward if the electric field is directed downward. The magnitude of the electric field is $3.3\times 10^6~N/C$ and it is directed downward.
