14.A solid sphere of radiusR carries a total charge Q, uniformly distributed in the volume of...

 

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14.A solid sphere of radiusR carries a total charge Q, uniformly distributed in the volume of the sphere. (a) What is the charge density? (b) Employ Gauss's dielectric flux theorem to caleulate the electric field inside the sphere, at distance r<R from the center of the sphere. Provide a drawing showing relevant surfaces and distances. (c) What is the electric field outside the sphere, at distance r>R from the center of the sphere? (Showing a derivation is not necessary.) (d) Using your expressions for the electric field, find the electric potential V (r), outside the sphere and inside the sphere. 15. A ball of known charge g and unknown mass m, initially at rest, falls freely from a height h in a uniform electric field E that is directed vertically downward. The ball hits the ground at a speed v 16. Derive the capacitance for:(a) A parailel plate capacitor with cross-sectional area A and plate separation d: (b)A cylindrical capacitor with inner conductor radius a, outer conductor radius b, and length L. (where L » b-a); 2vgh. Find m in terms ofE, q and g. 14.A solid sphere of radiusR carries a total charge Q, uniformly distributed in the volume of the sphere. (a) What is the charge density? (b) Employ Gauss's dielectric flux theorem to caleulate the electric field inside the sphere, at distance r<R from the center of the sphere. Provide a drawing showing relevant surfaces and distances. (c) What is the electric field outside the sphere, at distance r>R from the center of the sphere? (Showing a derivation is not necessary.) (d) Using your expressions for the electric field, find the electric potential V (r), outside the sphere and inside the sphere. 15. A ball of known charge g and unknown mass m, initially at rest, falls freely from a height h in a uniform electric field E that is directed vertically downward. The ball hits the ground at a speed v 16. Derive the capacitance for:(a) A parailel plate capacitor with cross-sectional area A and plate separation d: (b)A cylindrical capacitor with inner conductor radius a, outer conductor radius b, and length L. (where L » b-a); 2vgh. Find m in terms ofE, q and g.