Prove that the component of the electric field strength perpendicular to the surface of a uniformly charged section of the plane is equal to E ⊥ = 4πϵ0σΩ, where Ω — solid angle under which one sees this region from the considered point in space, σ is the surface charge density. Using this method, determine the electric field strength: a) in the center of a cube, five faces of which are uniformly charged with a surface charge density σ, and one face is not charged; b) in the center of a regular tetrahedron, three faces of which are charged with a surface density σ1, and the fourth — with a surface charge density σ2; c) uniformly charged with a surface charge density σ1; d) on the axis of a long pipe with a cross-section in the form of a regular triangle, if the surface charge density of the faces of the triangle of the pipe is equal to σ1, σ2, σ3, respectively; e) at the vertex of a cone with an angle at the vertex α and a height h, uniformly charged with a volume charge density ρ; f) on the edge of a long bar uniformly charged with a volume charge density ρ; the cross-section of the bar is a regular triangle with side l.