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A long charged cylinder of linear charged density à is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders ? |
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Answer» <P> Solution :Let A be a long charged cylinder of linear charge density ^ and B be a hollow co-axial conductingcylinder. Charges are induced on B as shown in Fig. 2.08. Let us find electric field at a point P in the space between the TWO cylinders SITUATED at a distance r from axis of cylinders.To find `vecE` at point P consider a cylinder of length land radius r as the Gaussian surface. Obviously total electric FLUX over the surface `phi_E = int vecE.hatn ds = E pi rl...(i)` According to Gauss.s theorem, the electric flux `phi_E = 1/epsi_0` (charged enclosed) `= 1/epsi_0.(lambda I)`...(ii) Comparing the values of electric flux given by (i) and (ii), we have `E 2pi rl= (lambda I)/(epsi_0) rArr E = lambda/(2pi epsi_0 r)` Obviously, the electric field is radial i.e., field is directed outward perpendicular to the charged cylinder. 
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