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An oil droplet of radius r and density ρ remains at rest in a uniform electric field E directed vertically upward. If the density of air is ρ0, with ρ0 > ρ, and e is the elementary charge, the droplet must have—

1. an excess of 4πr³(ρ−ρ0)g / 3Ee electrons
2. an excess of 4πr³(ρ−ρ0)g / eE electrons
3. a shortage of 4πr³(ρ−ρ0)g / 3eE electrons
4. a shortage of 4πr³(ρ−ρ0)g / eE electrons

Correct answer: an excess of 4πr³(ρ−ρ0)g / 3Ee electrons

Solution

For equilibrium the electric force balances net gravity minus buoyancy: |q|E = (4/3)pi r^3 (rho0 - rho) g. Since rho0 > rho the charge must be negative, so the drop has an EXCESS of n = 4 pi r^3 (rho0-rho) g /(3 E e) electrons.

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