Consider an oil droplet of mass m and charge q. We want to determine the charge on the droplet in a Millikan-type experiment. We will do this in several steps. Assume, for simplicity, that the charge is positive and that the electric field between the plates points upward.a. An electric field is established by applying a potential difference to the plates. It is found that a field of strength E_0?will cause the droplet to be suspended motionless. Write an expression for the droplet??s charge in terms of the suspending field E₀and the droplet??s weight mg.b. The field E₀is easily determined by knowing the plate spacing and measuring the potential difference applied to them. The larger problem is to determine the mass of a microscopic droplet. Consider a mass m falling through a viscous medium in which there is a retarding or drag force. For very small particles, the retarding force is given by F_drag= -bv where b is a constant and v the droplet??s velocity. The sign recognizes that the drag force vector points upward when the droplet is falling (negative v). A falling droplet quickly reaches a constant speed, called the terminal speed. Write an expression for the terminal speed v_termin terms of m, g, and b.c. A spherical object of radius r moving slowly through the air is known to experience a retarding force F_drag= -6πηrv where η is the viscosity of the air. Use this and your answer to part b to show that a spherical droplet of density ρ falling with a terminal velocity v_termhas a radius

d. Oil has a density 860 kg/m³. An oil droplet is suspended between two plates 1.0 cm apart by adjusting the potential difference between them to 1177 V. When the voltage is removed, the droplet falls and quickly reaches constant speed. It is timed with a stopwatch, and falls 3.00 mm in 7.33 s. The viscosity of air is 1.83 × 10^-5 kg/m s. What is the droplet??s charge?e. How many units of the fundamental electric charge does this droplet possess?

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