Question

1. A metal sphere of radius a is surrounded by a thick concentric metal shell (inner radius b, outer radius c, as shown in fig. I). Neither the shell nor the sphere carries any charge, but there is a point charge Qlocated inside an irregularly shaped cavity in the otherwise solid sphere. The irregular cavity is not concentric with the sphere. a) Make a reasonable sketch of the induced charges on all the surfaces, spacing equally those that must be distributed uniformly, and reasonably concentrating those that are not. b) What is the electric field in the region a r b? c) The shell is now grounded, as shown in I Make a reasonable sketch of the induced charges on all the surfaces, with the same level of care needed for a). d) What is the electric field in the region r >c in case II?

Answer 1

For part - a & b thetaprime = theta [where not grounded] for a < r < b using Gouss�s law take an Gaussion sphere of radius �r� [a < r < b] integral E^rightarrow middot n^hat ds = Qenclosed/60 E ds = + theta - theta + theta/60 = > E = theta/4 pi r^2 elementof_0 E^rightarrow = theta/4 pi elementof_0 r^2 for a < r < b It outer radius of shell is grounded then potential at(r = c) must be zero so V_c = thetaprime/4 pi elementof_0 c - theta/4 pi elementof_0 c + theta/4 pi elementof_0 c - theta/4 pi elementof_0 c + theta/4 pi elementof_0 c v_c = 0 = thetaprime/4 pi elementof_0 c = > thetaprime = 0 \r\n Because Sketch is some as infig (1) expt in this case (theta prime = 0) for r > c using Gauss�s law [Gauss�s law sphere of leading �r�]