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Quiz02_solutions

# Quiz02_solutions - Physics 222 Quiz 2 Solutions Fall 2011...

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Physics 222 Quiz 2 Solutions Fall 2011 Question 1 Quizzes 2A and 2C Electric charge is distributed uniformly along an infinitely long, thin wire. The charge per unit length is λ>0. By applying Gauss's law determine the magnitude of E(r), the electric field at a distance r from the line charge. (Show your work.) Solution: We have cylindrical symmetry. Because of that electric field does not have any component parallel to the wire and also it does not have any component tangent to a circle in a plane perpendicular to the wire with its center on the wire. The only nonzero component is directed radially outward from the wire at each point. The field lines are radial and lie in planes perpendicular to the wire. The convenient choice for a Gaussian surface is a cylinder with arbitrary radius r and arbitrary length l, with its ends perpendicular to the wire. There is no flux through the flat ends where the perpendicular component is zero, 0 = E .

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