A small section of an infinitely long charge distribution is shown at right. A l

Question

A small section of an infinitely long charge distribution is shown at right. A line charge of linear charge density ?(line) = 1.5 nC/m is at the center. It is surrounded by an inner cylinder is made from insulating material, which has a radius of 1.5 cm, and has a volume charge density given by ?(inner). The outer cylindrical shell is made of a conducting material, of inner radius 5 cm and outer radius 6 cm. The outer cylindrical shell has an overall charge per unit length given by ?(outer) = -2.5 nC/m.Suppose the inner cylinder had a uniform charge density of ?(inner)= 2.8

Explanation / Answer

Try to use Gauss's Law and what you know about how charges act in conductors (like charges repel each other). Look at the problem: it says "very long" meaning that the length of the tube is much greater than the radius. This will let you make important conclusions later on. The line of charge in the center carries a total charge of al (I'm using a for charge density and l for length). The TOTAL charge on the conducting tube is also al. The positive charge from the line of charge will attract the negative charge in the tube, therefore a negative charge -al will be on the inside of the conducting tube. The positive charges in the conducting tube repel each other, therefore, they will want to be as far away from each other as possible, so a charge of 2al will reside on the outside of the tube. (The charge on the outside must be 2al because 2al + -al = al) Now, Gauss's Law states that the Electric Field times the area through which it acts (basically electric flux) is proportional the the charge enclosed by the surface. The equation is E*A=q/e. (e is the value for the permittivity of free space). So let's choose a cylinder as the Gaussian surface that we will use to find out the electric field in each area. Imagine a cylinder concentric with the line of charge of radius r

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