Consider a segment of angle α < π/2 of a circle of radius R. There is a dipolar layer on the circular arc of the circle

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Consider a segment of angle α < π/2 of a circle of
radius R. There is a dipolar layer on the circular arc of the
circle segment and no charge inside the segment.

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α R Dipolar Layer
a) Show that the given electrostatic potential in cylindrical coordinates, α Sp/a sin (I._) + 3/27/a sin (26) "SR, VE [0,a], p <, SE , or,y) = otherwise. {7" = solves the Poisson equation Aø(r, 4) = 0 inside of the segment and specify the boundary conditions of this boundary value problem. b) Compute the electric field Ē (F") inside of the segment. c) Calculate the surface charge density o(ñ) on the boundaries of the circle segment as well as the dipole moment D() of the dipolar layer.