An experiment is performed to measure the charge of the electron. Negatively charged oil droplets are sprayed from an atomiser into the gap between two horizontal metal plates. A potential difference is applied, and one of the droplets remains stationary.
Identify the forces acting on the stationary droplet. In your answer you should state the relationship between the forces. (The upthrust on the droplet due to the air it displaces is negligible).
The potential difference between the plates is then changed to zero, and this droplet falls at a terminal velocity of 1.5×10−4 m s−11.5 \times 10^{-4} \text{ m s}^{-1}1.5×10−4 m s−1.
Show that the radius of the droplet is approximately 1.2×10−6 m1.2 \times 10^{-6} \text{ m}1.2×10−6 m. Assume that the droplet is spherical and use g=9.81 m s−2g = 9.81 \text{ m s}^{-2}g=9.81 m s−2.
The potential difference between the plates is restored to its initial value and the droplet becomes stationary again. The charge on the droplet is −8.0×10−19 C-8.0 \times 10^{-19} \text{ C}−8.0×10−19 C.
A student suggests that, if the droplet splits into two spheres of equal size, both spheres could remain stationary in the same electric field.
Deduce whether this suggestion is correct. (Take the elementary charge to be e=1.6×10−19 Ce = 1.6 \times 10^{-19} \text{ C}e=1.6×10−19 C.)
