Question

Flux and nonconducting shells. A charged particle is suspended at the center of two concentric spherical shells that are very thin and made of nonconducting material. Figure (a) shows a cross section. Figure (b) gives the net flux ? through a Gaussian sphere centered on the particle, as a function of the radius r of the sphere. The scale of the vertical axis is set by ?_s = 19.0

Answer 1

the region 0<r<4 inside sphere A;
Gauss says: ? =?ds*E(?,?,r), WHERE
ds*E(?,?,r) is dot product of 2 vectors ds and E(?,?,r),
|ds|=r*sin?*d?*r*d? is elementary area on a sphere with radius r in spherical coordinate system, direction of ds being normal to the sphere,
|E(?,?,r)|=-q/(4?*?0*r^2) is strength of electric field produced by a point charge q in the center, direction of E being normal to the sphere, ?0=8.854e-12 is const,
angle ? is measured around z-axis as 0<=?<2?,
angle ? is measured from plane XOY as