SECTION B 3. A uniformly charged non-conducting thin circular disk of radius R and surface charge density is located in the x - y plane with its centre at the origin of a right handed Cartesian co-ordinate system. (i) Calculate the electric potential due to the disk along the +z axis [8 marks] (ii) From the above result or otherwise show that the electric field at a point on the z axis is given by E = σ 20 -(1-cosa)k (1 where a is the angle at which the edge of the disk is seen from the observation point on axis [6 marks] (iii) From the above result derive an expression for the electric field when the radius of the disk becomes much larger than the observation distance. Comment on your result. [2 marks] (iv) From the result obtained in point (ii) above derive an expression for the electric field when the radius of the disk is much smaller than the observation distance. Comment on your result. (v) Show that the electric potential at (x, 0, 0) for x > R is given by [3 marks] R 2 V(x, 0, 0) = ΑΠΕ 00 pdpdo x²-2px cos but DO NOT attempt to evaluate the integral. [3 marks] (vi) Show that V(x, 0, 0) for x R approximates the potential due to a point charge [3 marks] [Total 25 marks]