Question

l ve a copy of this Calforsis, 94l0s, USA Question 1. [25 points] A sperical shell has a potential given by V Vo (cos θ + 3 cos 2θ-1). Use separation of variables to answer the following . 15 points] Write the general expression for the potential inside the shell. Explain i [5 points] Write the general expression for the patential outside the shell. Explain i 15 points) Write down allthe boundary conditions for this situation iv. [5 points) Determine the exact equation (obtaining all coefficients) for the potential outside the shell. Hint: Rewrite the pot on the shell as Legendre Polynomials. v. 5 points] Determine the charge density, o, on the shel. Question 2. [25 points] A very long cylinder placed along the z axis (coming out of the pagel, with radius R and magnetization M = kszg. There is no free current. (k is a constant.) i. 19 points] Determine the bound volume and surface current. (In your answer i. [8 points) Determine H(the auxiliary field), at a point in the material, a distance s ii. 8 points) Determine B (magnetic field) at a point in the material, a distance s include the direction of any bound currents.) from the center (scR). from the center (s<R), Question 3. [25 points] The figure at right shows a shaded insulating shell (with inner radius a

please do #1 show short steps

Answer 1