Question

8. A long coaxial cable (Fig 2b ) carries a uniform volume darge density ρ on the inner cylinder (radius a), and a uniform surface charge density ơ 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 nt Find the electric field in each of the three regions:) inside the nnr cylinder (s < a), (ii) between the cylinders (a < s < b), (iii outside the cable (s > b). Plot El as a function of s 9. An infinite plane carries a uniform surface charge σ. Use Gauss's law to find its electric field. 10. Two infinite parallel planes carry equal and opposite uniform charge densities ±σ. Find the field in each of the three regions: (i) To the left of both, (i) between them (iii) to the right of both. Figure 2: Diagram for Problem 8

Answer 1

For s < a take a Gaussian surface of radius s < a and length Then using Gauss law oint E^bar middot ds^Vectyor = q_enclosed/epsilon_0 = > E middot 2 oi s middot l = 1/epsilon_0 integral p dJ = rho/epsilon_0 integral^s_0 s ds integral^2 pi_0 d phi integral^l_0 dz = rho/epsilon_0 s^2/2 2 pi l E 2 pi s = rho/epsilon_0 pi s^2 E^Vector = rho s/2 epsilon_0 s^Hat s < a Now for a < s < b we take a Gaussian surface of (a < s < b) for radious s and length l Use Gauss law oint E^bar middot ds^Vector = q_enclosed/epsilon_0 = > E middot 2 pi s l = rho/epsilon_0 pi s^2 l E^Vector = rho s/2 epsilon_0 s^Hat, (a < s < b) \r\n For s > b we take a Gaussian surface of radious s > b and length l then total enclosed charge = 0 so use Gauss law