You may have seen a \"coaxial cable\" connected to a television set. As shown in

Question

You may have seen a "coaxial cable" connected to a television set. As shown in Figure 22.107. a coaxial cable consists of a central copper w ire of radius r, surrounded by a hollow copper tube (typically made of braided copper wire) of inner radius r_2: and outer radius r_3. Normally the space between the central wire and the outer tube is filled with an insulator, but in this problem assume for simplicity that this space is filled with air. Assume that no current runs in the cable. Suppose that a coaxial cable is straight and has a very long length l, and that the central wire carries a charge +Q uniformly distributed along the wire (so that the charge per unit length is + Q/l. everywhere along the wire). Also suppose that the outer tube carries a charge -Q uniformly distributed along its length L The cylindrical symmetry of the situation indicates that the electric field must point radially outward or radially inward. The electric held cannot base any component parallel to the cable. In this problem, draw mathematical Gaussian cylinders of length d (with d much less than the cable length L) and appropriate radius r. centered on the central wire. Use a mathematical Gaussian cylinder located inside the central wire (r

Explanation / Answer

a) charge on inner conductor = Q * [(2pi * r1)/L]

     charge on outer conductor = Q * [(2pi * r2)/(2pi * r3)]

                                                 = Q * [(r2)/(r3)]

b)   Electric field = [1/(4pi * eo)] * Q * [(r1)/(r2)]/r2

c)   Electric field = [1/(4pi * eo)] * Q * [(r2)/(r3)]/r2

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