59. On two concentric spheres of radius R and 2R, charges are uniformly distributed with surface densities σ1 and σ2.
Required: 1) using the Ostrogradsky - Gauss theorem, find the dependence E(r) of the electric field strength on the distance for three regions: I, II, III, take σ1 = −2σ, σ2 = σ; 2) calculate the tension E at a point remote from the axis of the cylinders at a distance r, and indicate the direction of the vector E. Take σ = 0.4 mC/m2, r=3R;
3) plot E(r).

Detailed solution. Decorated in Microsoft Word 2003. (Target decided to use formula editor)