The charge of an electron was first measured by the American physicist Robert Mi

Question

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 10-4mm in diameter, into a space between two parallel horizontal plates separated by a distance d. A potential difference V_AB is maintained between the 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 will remain at rest between the plates if the magnitude of its charge is: q= 4pi/3(pr^3gd)/V_AB where p= density of oil Ignore the buoyant force of the air. By adjusting V_AB to keep the drop at rest, the charge on that drop can be determined provided its radius is known. (b) How do think Millikan used the answer to (a) in his experiment?

Explanation / Answer

Here ,

electric field = potential difference /distance

electric field = V_AB/(d)

let r is the radius of the drops ,

for the drops to be suspened in air ,

electric force on drop = gravtity force

mass * g = q * E

(4/3) * pi * r^3 * p * g = q * V_AB/d

q = (4pi/3)*(p r^3g d)/V_AB

b)

using the results in answer (a)

he found the smallest charge acquired by the oil drops

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