P400. We wish to find the right shape of Gaussian surface to have a constant fie
ID: 1883103 • Letter: P
Question
P400. We wish to find the right shape of Gaussian surface to have a constant field perpendicular to it (easy to find flux) for an infinitely long line of charge that is distributed so that it is uniformly 0.5 Coul/meter. To help you imagine this, think of the infinitely long line of charges as if it were an infinitely long sausage tube full of paint with an explosive string centered inside a) Which of the following surfaces would most nearly get an even coat of paint? a sphere? A cylinder? a cube? b) How could you tell? What characteristic of the surface made it win your vote in a)? c) Label your Gaussian shape with the appropriate variables, and Identify what you need to know of these to find the amount of charge (paint) that is inside. Iea sphere would be labeled with an r, a cylinder with an r & 1, while a cube is labeled with anl. d) Use Gauss' law to find the field at a location near the string of charges which is 1.5 meters from itExplanation / Answer
1. a cylinder would be the most appropriate one due to its symmetry present in it which resembles a line .
2.it has got both axial and radial symmetry and a line charge can well accomodate inside a cylinder which is left uncovered by two surfaces.
3. since it is a line charge so i assume that charge distribution is uniform and linear in nature so linear charge density (lambda)must be given in the question so total charge will be Q=labda x length of the finite rod.
4.total charge that has been already found in sub part 3,make use of that then this charge upon epsilon zero X (4x3.14xr2) where r will be 1.5m which is the radial distance from the line charge.
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