5) A thick spherical shell carries charge density p = , (a b. Plot [E| as a function of r, for the case b = 2a.
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- 1. The electric field in a region of space near the origin is given by () E(x, y, z) = Eo a (a) Evaluate the curl V x E(x, y, z) (b) Setting V(0, 0, 0) = 0, select a path from (0,0, 0) to (x, y,0) and compute V (x, y, 0).b) A uniformly charged rod has length L and charge Q as shown below. P a L (i) Find the electric field vector at point P above center of rod. The distance from center of rod to point P is a. (ii) Using the results from part (i) above, show that for an infinite rod (L → ∞) the electric field at point P is given by E = 2te,a where 1 = Q/L is the linear charge density.Find the magnitude of the electric field for r>b
- A solid sphere of radius a is concentric with a hollow sphere of radius b, where b > a. If the solid sphere has a uniform charge distribution totaling +Q and the hollow sphere a charge of –Q, the electric field at radius r, where r < a, is which of the following, in terms of k = (4π∈0)–1? Choose the correct answer. kQ/b2 zero kQ/a2 kQr/a3 kQ/r24. A cylindrical dielectric of permittivity &, radius R, and length h, is centered about the z-axis. Assume this Cylinder has a uniform electric polarization along its axis given by P = Poz. a) What are the polarization charge densities on its surfaces? b) What is the electric displacement vector D anywhere on its axis? c) What is the electric field vector E anywhere on its axis?A thick spherical shell carries charge density (rho) = k/r^2 for r1 ≤ r ≤ r2. Find the electric field in the three regions: (i) r < r1, (ii) r1< r < r2, (iii) r > r2. Plot the magnitude of E as a function of r, labeling clearly where r1 and r2 are.