You have to consider Gauss's law which says that the electric flux out of any closed surface is proportional to the charge enclosed by the surface regardless on the charge distribution.

Without more information, it sounds like in this case it is implied that volatility of the oil is sufficient to overcome any effect of the electric field or charge. As such, if the oil drop is able to expel molecules of oil, then those molecules would likely carry neutral charge.

Millikan used a similar set up in his oil drop experiment to determine the charge of the electron. His experiment was very sensitive to the mass of the oil which made him choose one with a low vapor pressure in order pass through the vacuum with minimal loss of mass due to evaporation.

You have to consider Gauss's law which says that the electric flux out of any closed surface is proportional to the charge enclosed by the surface regardless of the charge distribution.

Without more information, it sounds like in this case it is implied that volatility of the oil is sufficient to overcome any effect of the electric field or charge. As such, if the oil drop is able to expel molecules of oil, then those molecules would likely carry neutral charge.

Millikan used a similar set up in his oil drop experiment to determine the charge of the electron. His experiment was very sensitive to the mass of the oil which made him choose one with a low vapor pressure in order pass through the vacuum with minimal loss of mass due to evaporation.