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Statement of a problem № 41304

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The Millikan Oil-Drop Experiment The charge of an electron was first measured by the American physicist Robert Millikan during 1909-1913. In his experiment, oil is sprayed in very fine drops (around 10-4 mm in diameter) into the space between two parallel horizontal plates separated by a distance d. A potential difference V AB is maintained between the parallel plates, causing a downward electric field between them. Some of the oil drops acquire a negative charge because of frictional effects or because of ionization of the surrounding air by x rays or radioactivity. The drops are observed through a microscope. (a) Show that an oil drop of radius r at rest between the plates will remain at rest if the magnitude of its charge is q = 4π/3 pr3gd/ V AB Where p is the density of the oil (ignore the buoyant force of the air.) By adjusting V AB to keep a given drop at rest, the charge on that drop can be determined, provided its radius is known. (b) Millikan’s oil drops were much too small to measure their radii directly. Instead, Millikan determined r by cutting off the electric field and measuring the terminal speed v, of the drop as it fell. (We discussed the concept of terminal speed in Section 5.3.) The viscous force F on a sphere of radius r moving with speed u through a fluid with viscosity η is given by Stokes s law: F = 6πηru. When the drop is falling at uv the viscous force just balances the weight w = mg of the drop. Show that the magnit

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