PHYS 220 Midterm, Spring 2019

De op MK ay Lue Physics 220 ae Mid-term Exam Time : 2.5 hours 1. Sketch qualitatively the electric field lines ()_ for a conducting spherical shell with a net charge of -Q and a point charge +Q in the cavity off-center; t ER Af) same as i) but the shell is non-conducting and the -Q charge is smeared uniformly over the outer surface of the shell; fii) same as i), the spherical shell is conducting and has zero net charge; SEY ET, - Does the following picture represent a legitimate electrostatic fi eld (there is axial symmetry with respect to X axis)? Give reasoning. x< Le 7 - Uw ory ch S chee is — clo a Lomnkek (3A square of side! is formed by thin rods that carry a uniform linear density of charge A. Cor bac len! jeg . 27 a) Find the electric potential y(z) at height z from the plane of the square above its center, { cle vA lg 72 WA sc chee lg Scanned by CamScanner b) Sketch qualitatively the function p(z) for positive and negative z. We are specifically interested in the two limits: small distances |z| « | and large distances |z| >> c) A test charge particle of the opposite sign is confined to move in the z direction along the line rei through the center of the square. What can you say about the possible types of motion (the test particle has a mass; friction is negligible) _—— JX charge distribution has the symmetry of an [infinite cylinder| with the volume charge density of the form p(r) = py exp (- ) where r is the distance from the axis. Specifythe picture of the field and find the electric field strength E(r) as a function of r. ply) = Ys ero(-C¥ Vinad [i Ge chargé +Q is placed at distance d from an infinite conducting plane. w much external work is required to move the charge away from the plane to distance 2d? Compare the work obtained by integrating the force over a path to the change in “potential energy” of the charge-image pair. If the two quantities differ, which gives the correct answer, and what is wrong with the other? A sheet of charge with surface charge density ¢ is placed between two conducting slabs connected by a wir. The separation between slabs is L, the distance from the left slab to the sheet is x. Find the induced surface charge densities 0, and density 02 on the slabs. Hints: Image method not helpful; Gauss good; wire important. L ed od Se ale Ka a Van de Graaf generation rubber belt 0.3 m wide travels at a velocity of 20 m/s. The belt is given a surface charge at the lower roller, the surface charge density being such that the electric field strength is 10° V/m on each side of the belt. . Find the current produced by the moving belt. 4 t | Ko a certain region in space, there are 10'7 doubly charged positive ions per m? moving east with a speed of 10° m/s, and also 10'® electrons per m’ moving south with a speed of 107 m/s. Find the magnitude and direction of the current density vector. \ Is the current density large compared to that in a typical wire carrying I A current? Scanned by CamScanner