A very long hollow cylinder has inner radius a and outer radius b and carries charge per unit length +a, where a is a positive constant with units C/m. A line of charge lies along the axis of the tube and has charge per unit length +a. (a) Calculate the electric field in terms of a and distance r from the axis of the tube for (i) r > a; (ii) a < r < b; (iii) r > b. (b) What is the charge per unit length on (i) the tube's inner surface and (ii) the tube's outer surface? Hint:This problem is really a series of conceptual questions but the answers are equations. You must answer part (b) before you can answer the three sub-parts of part (a).
A very long hollow cylinder has inner radius a and outer radius b and carries charge per unit length +a, where a is a positive constant with units C/m. A line of charge lies along the axis of the tube and has charge per unit length +a.
(a) Calculate the electric field in terms of a and distance r from the axis of the tube for
(i) r > a;
(ii) a < r < b;
(iii) r > b.
(b) What is the charge per unit length on
(i) the tube's inner surface and
(ii) the tube's outer surface?
Hint:This problem is really a series of conceptual questions but the answers are equations. You must answer part (b) before you can answer the three sub-parts of part (a).
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