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Unformatted text preview: PHY 2049 FALL 2000 EXAM 1 (MAKEUP) 1. A sphere of radius R with a spherical cavity of radius R/ 2, as shown, is charged with a uniform charge density ρ . Find the electric field at the point P at a distance R from the center of the sphere on the same side where the cavity is. Hint: A uniformly charged sphere with a cavity can be viewed as a superposition of two spheres: a solid sphere of radius R without a cavity and uniformly charged with a charge density ρ and a smaller sphere of radius R/ 2 uniformly charged with a charge density − ρ . In the place where the two spheres overlap, one would equivalently get a zero charge density. Volume of a sphere of radius r is 4 3 πr 3 . Answer: 2 πρkR/ 3 R P R The electric field on the surface of a sphere of radius R and charge Q is E sphere = kQ/R 2 . The charge is related to the charge density and the volume of the sphere Q = ( ρ )(4 πR 3 / 3). This gives E sphere = kQ R 2 = k R 2 ρ 4 πR 3 3 = 4 πkρR 3 . E 1 is the electric field at the surface of a uniformly charged sphere of radius R and charge density ρ . E 2 is the electric field at a distance R exterior to a sphere of radius R/ 2 and charge density − ρ . Using the general expression for the electric field at the surface of a sphere, the net electric field is E = E 1 + E 2 = 4 πkρR 3 + 4 πk ( − ρ ) R 2 3 = 4 πkρR 3 − 2 πkρ 3 = 2 kρπR 3 . 2. An atom of hydrogen is a proton with an electron orbiting it along a circular path of diameter d = 10 10 m. What must be the velocity of an electron so that it could remain on this orbit? Express the answer in terms of the speed of light c = 3 × 10 8 m/s. Hint: the centripetal acceleration for a particle moving with velocity v along a circular orbit of radius r is a = v...
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 Spring '08
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 Physics, Electron, Charge, Electric charge

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