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- Use Gauss's Law for the following: A conductor with cavities is shown in cross-section along with some pointcharges in the hollow spaces inside. The net charge on the conductor itself, qcond, is givenbelow each figure. Determine the amount of charge on the surface, inside and out, andsketch the charge distribution on the surface. (See picture)R OI A very thin spherical plastic shell of radius R = 18 cm carries a uniformly distributed negative charge of Q = -8 nC on its outer surface. An uncharged solid metal block is placed nearby. The block is w = 9 cm thick and is 9 cm away from the surface of the sphere. Calculate the magnitude of the elec- tric field at the exact center of the conductor generated only by the polarization of the con- ductor. In other words, do not include the electric field generated by the sphere. Answer in units of N/C.$ Q2/Evaluate D.ds side of the divergence theorem for the field D = 2xyax + x'yay C/m² and the rectangular parellelepiped formed by the planes x = 0 and 1, y = 0 and 2, and z = 0 and 4.
- What would the final speed be (infinitely far away) of a charge of +q and mass, m, if released at rest from the edge of a fixed , uniformly charged disk of radius a and total charge Q? The thickness of the disk is irrelevant.A thin conducting cylindrical shell of radius a, carries a surface charge density o> 0 (the thick- ness of the shell can be neglected). Based on Gauss Law the electric field due to this cylinder is given by SE b) Inside the cylinder r a Determine the corresponding electric potential V(r) as a function of r and relative to a fixed arbitrary reference point A (i.e. rA) for a) Outside the cylinder, at a particular distance r, r > a.Charge is distributed uniformly with a density ρ throughout an infinitely long cylindrical volume ofradius R. Show that the field of this charge distribution is directed radially with respect to the cylinder.