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. e. Suppose the outer conducting shell were grounded. How would the electric fields in the various regions and the charge per unit length on the inner and outer surfaces of the conducting cylinder be affected? Would they change or remain the same? Explain your answer using Gauss

Explanation / Answer

The electric field of an infinite line charge with a uniform linear charge density can be obtained by a using Gauss' law. Considering a Gaussian surface in the form of a cylinder at radius r, the electric field has the same magnitude at every point of the cylinder and is directed outward. The electric flux is then just the electric field times the area of the cylinder. The electric field of an infinite cylindrical conductor with a uniform linear charge density can be obtained by using Gauss' law. Considering a Gaussian surface in the form of a cylinder at radius r > R, the electric field has the same magnitude at every point of the cylinder and is directed outward. The electric flux is then just the electric field times the area of the cylinder.

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