Question

Situation 1: You have a metal cube, measuring L on each side. The metal is in electrostatic equilibrium and has a net 4. charge of Q,. The cube has a cavity within it, however-where there is no metal. The shape of this cavity is not known. Somewhere within the cavity rests a point charge, q,. Its exact location is unknown, but it is not in contact with the inner wall of the cavity At a certain point P, on the outer surface of the cube, the surface charge density is 25% greater than the average charge density for the cube's entire outer surface Situation 2: You have removed situation 1 entirely, and instead.... You have a sphere of outer radius Rs, made of insulative plastic material. It is solid plastic except for a perfectly spherical cavity of radius R, centered within it-where there is no plastic at all The plastic is in electrostatic equilibrium and has a net charge distribution described by p(r)-ar5 (only for RcsrsR) At the center of the cavity space rests a point charge, q. Point P is located within the plastic at a distance r from the sphere's center he electric field magnitude at point P2 is the same as at point P, in situation 1 A particle of mass m, and charge q, is orbiting the sphere at constant speed v,, maintaining a distance r above the sphere's outer surface. Situation 3: You have removed situation 2 entirely, except for the particle. Now, instead.... You have a infinitely wide, solid slab of plastic (insulative) material of thickness H This slab is fixed in position so that it is parallel to, and bisected by, the x-z plane. (Thus, the plastic exists throughout the region -H/2 s y s H/2 only) This plastic slab is in electrostatic equilibrium and has a net charge distribution described by p(y)-byc (only for -H/2 s y s H/2) Suppose you now launch the particle (release it to move freely) at the point (0, 3r, 0) with an initial velocity [v,, 0,0]. At what point (give the x-y-z coordinates) will the particle strike the slab? Notes:Neither air nor gravity play any role in any part of this entire problem The After Class 08 materials offer several situations involving non-uniform volumetric charge densities- including how to use dq-ρdV for various geometries situations Watch your units carefully throughout this entire problem R. - 2.10 mm The data: L - 9.87 mm R.-7.40 mm r5.96 mm H- 9.38 mm Q, - 4.51 nC a,2.36 nC 5.72 nC*146 nC C/m3 m-4.39 x 10-19 kg ,-8.85 x 10-12C9(N. m ) b _ _ 1.60 C/m c--720

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