Answer
Since the required number of excess electrons is $~~1.8\times 10^{17},~~$ this experiment seems impractical.
Work Step by Step
The electrostatic force on the sphere must be equal in magnitude to the weight of the sphere, and the electrostatic force must be directed upward.
Since the direction of the electric field is downward, the charge on the sphere must be negative.
We can find the magnitude of the required charge:
$F = q~E = 4.4~N$
$q = \frac{4.4~N}{E}$
$q = \frac{4.4~N}{150~N/C}$
$q = 0.029~C$
The required charge on the sphere is $~~-0.029~C$
We can find the required number of excess electrons:
$\frac{-0.029~C}{-1.6\times 10^{-19}~C} = 1.8\times 10^{17}$
Since the required number of excess electrons is $~~1.8\times 10^{17},~~$ this experiment seems impractical.
