To find the potential difference (V) between the plates required to hold the droplet in equilibrium, we need to consider the forces acting on the droplet.
1. Gravity Force (Fg):
The force of gravity (Fg) acting on the droplet is given by the equation Fg = mg, where m is the mass of the droplet and g is the acceleration due to gravity.
Given:
Density of oil (ρ) = 860 kg/m^3
Diameter of droplet (d) = 0.67 μm = 0.67 × 10^-6 m
To find the mass (m) of the droplet, we can use the equation m = ρ × V × d, where V is the volume of the droplet.
The volume of the droplet (V) can be calculated using the equation V = (π/6) × d^3.
Substituting the given values, we can calculate the mass (m) of the droplet.
2. Electric Force (Fe):
The electric force (Fe) acting on the droplet is given by the equation Fe = qE, where q is the charge on the droplet and E is the electric field between the plates.
Given:
Charge on the droplet (q) = +e (where e is the elementary charge)
Distance between the plates (d) = 4.0 mm = 4.0 × 10^-3 m
To find the electric field (E), we can use the equation E = V/d, where V is the potential difference between the plates.
Since the droplet is in equilibrium, the electric force (Fe) must be equal to the gravity force (Fg), i.e., Fe = Fg.
Substituting the expressions for Fe and Fg, we get:
qE = mg
Now, substituting the expressions for q, E, and m in terms of the given values, we can solve for V.
Note: The value of the elementary charge (e) is 1.6 × 10^-19 coulombs.
Let's put all the values together and calculate the potential difference (V).