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6. A cylinder with radius R and infinite length is centered on the z-axis and has a uniform charge density Po r < R r> R p= where po is a constant. a) Using Gauss's law find the electric field for r < R and r > R. Express your answer in terms of the charge per unit length of the cylinder (you'll have to think about how to define it). Hint: in terms of symmetry, this case is very similar to an infinite line charge. b) Now a uniform surface charge density o is pasted onto the surface of the cylinder such that the electric field outside the cylinder is zero. What is o in terms of R, po, and numerical factors?

6. A cylinder with radius R and infinite length is centered on the z-axis and has a uniform charge density Po r < R r> R p= where po is a constant. a) Using Gauss's law find the electric field for r < R and r > R. Express your answer in terms of the charge per unit length of the cylinder (you'll have to think about how to define it). Hint: in terms of symmetry, this case is very similar to an infinite line charge. b) Now a uniform surface charge density o is pasted onto the surface of the cylinder such that the electric field outside the cylinder is zero. What is o in terms of R, po, and numerical factors?

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6. A cylinder with radius R and infinite length is centered on the z-axis and has a uniform charge density r < R r> R p= Po 0 where po is a constant. a) Using Gauss's law find the electric field for r < R and r > R. Express your answer in terms of the charge per unit length of the cylinder (you'll have to think about how to define it). Hint: in terms of symmetry, this case is very similar to an infinite line charge. b) Now a uniform surface charge density o is pasted onto the surface of the cylinder such that the electric field outside the cylinder is zero. What is o in terms of R, po, and numerical factors?
Transcribed Image Text:6. A cylinder with radius R and infinite length is centered on the z-axis and has a uniform charge density r < R r> R p= Po 0 where po is a constant. a) Using Gauss's law find the electric field for r < R and r > R. Express your answer in terms of the charge per unit length of the cylinder (you'll have to think about how to define it). Hint: in terms of symmetry, this case is very similar to an infinite line charge. b) Now a uniform surface charge density o is pasted onto the surface of the cylinder such that the electric field outside the cylinder is zero. What is o in terms of R, po, and numerical factors?
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