Relationships Between Force, Field, Energy, Potential Video Lessons

Concept

# Problem: 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 E0 will cause the droplet to be suspended motionless. Write an expression for the droplet's charge in terms of the suspending field E0 and the droplet's weight mg.b. The field E0 is 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  falling through viscous medium in which there is a retarding or drag force. For very small particles, the retarding force is given by Fdrag = -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 vterm. Write an expression for the terminal speed vterm in terms of m, g, and b.

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###### Problem Details

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 E0 will cause the droplet to be suspended motionless. Write an expression for the droplet's charge in terms of the suspending field E0 and the droplet's weight mg.

b. The field E0 is 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  falling through viscous medium in which there is a retarding or drag force. For very small particles, the retarding force is given by Fdrag = -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 vterm. Write an expression for the terminal speed vterm in terms of m, g, and b.