Q3. A long coaxial cable (see Fig. 3) carries a uniform volume charge density ? on the inner cylinder (with radius a) and a uniform surface charge density on the outer cylindrical shell (radius b). This surface charge is negative and of just the right magnitude so that the cable as a whole is electrically neutral. Find the electric field in each of the following 3 regions: (a) inside the inner cylinder (s < a) (b) between the cylinders (a < s < b) (c) outside the cable (s > b) From these results, plot |E| as a function of s. Figure 3: A long co-axial cable of volume charge.
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Step 1:** For region (a) inside the inner cylinder (s < a), the electric field is given by: \[ \vec{E} = \frac{\rho a^2}{2\epsilon_0} \hat{r} \] ** Show more…
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'long coaxial cable carries a uniform volume charge density p on the solid inner cylinder (with radius a) and a uniform surface charge density o on the outer cylindrical shell (at radius b): The volume charge density of the inner cylinder is positive, and the surface charge density of the outer shell is negative, and of just the right magnitude such that the entire cable is electrically neutral (has no net charge one common way coaxial cables are used): a) Find the electric field in each of the following regions: Inside the inner cylinder (r < a) ii_ Between the two cylinders (a < r < b) iii. Outside the cable (r > b) Your answers should be in terms of the variables given, and fundamental constants_ b) Plot the magnitude of electric field |E| as a function of r'
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The Coaxial Cable. A long coaxial cable consists of an inner cylindrical conductor with radius $a$ and an outer coaxial cylinder with inner radius $b$ and outer radius $c .$ The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a uniform positive charge per unit length \lambda. Calculate the electric field (a) at any point between the cylinders a distance $r$ from the axis and (b) at any point outside the outer cylinder. (c) Graph the magnitude of the electric field as a function of the distance $r$ from the axis of the cable, from $r=0$ to $r=2 c$ . (d) Find the charge per unit length on the inner surface and on the outer surface of the outer cylinder.
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