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Section B.1 Consider a long thin wire of radius a carrying an electric charge à per unit length. a) Using Gauss' law or otherwise, show that the E field outside such a wire is A E(r) = -ep Σπειρ where p is the radial distance from r to the wire. Comment on any symmetry assumptions you make. Derive an expression for the electrostatic potential V(p). [6] b) Describe how the methods of images is used to solve electrostatic problems with boundary conditions. [3] c) Now consider the wire positioned above a conducting slab. The slab is in the ry plane at z ≤ 0, and the wire points along the r-axis, with its central axis at y = 0 and z = b > a. Using an appropriate image wire inside the conducting slab, derive an expression for the potential V(r) outside the wire in the region z > 0. Verify that V(r) fulfils the boundary conditions. Sketch the field lines in the yz plane. [7] d) Show that the induced surface charge density at the slab surface is X b o(x, y) = = π y² +62 PAGE 2 PIUNTED: MONDAY 1 APRIL, 2019 Continued overleaf... [4]