Question 1. A sphere of radius R contains charge with distribution given (in spherical coordinates) by: p(F") = k sin e' cosp' where k is a constant. (a) Determine the monopole total charge Q for this distribution (b) Determine the dipole moment for this distribution

There are 3 thin conductive infinitly thin spherical shells with a charge on each shell of +2Q. The innermost shell has a radius of R. Another of the shells has a radius of 2R. The outermost shell has a radius of 3R.  Draw a graph of E vs R. Make sure to show the values of E(3R), E(2R), and E(R).  Note: (put R on the x axis)

A total amount of positive charge Q is spread onto a thin non-conducting circular annulus of inner radius a and outer radius b. The charge is distributed in a way so that the charge density per unit area is given by ? =??3, where r is the distance from the center of the annulus to any point on it and k is a constant.(a) Find an expression for the total charge Q on the annulus. (b) Find an expression for the potential V at the center of the annulus in term of Q, a and b

Two spherical, hollow conductors are concentrically nested as shown in the cross-sectional diagram below and electrically isolated from each other. A net charge of -3 nC is divided between the conductors, with a total of -12 nC on the inner conductor and +9 nC on the outer one. The charges are, of course, free to move between the surfaces within each shell but cannot move from one shell to the other. The inner conductor has an inner radius of a=2 cm, outer radius of b=3 cm. The outer conductor has an inner radius of c=6 cm, an outer radius of d=8 cm. a (a) In equilibrium, all of the excess charge is found on the surfaces. Why is there no charge between a and b, nor between c and d? (b) Determine the net charge on each surface (ie how much charge is there at r = a, at r = b, at r = c and at r= = d). (c) Is the charge on the outer surface equal to the net charge on the outer container, the net charge of the system, or some other amount? Explain briefly. (d) Find the surface charge…