1. (a) Define the electric polarisation, P, and state its units. (3 marks) (b) Give the relationship between electric polarisation, P, and the electric field, E, applied to a material. (2 marks) (c) Describe, with a diagram, one mechanism by which a dielectric material can exhibit polarisation when subjected to an external electric field. (d) The piezoelectric coefficient of a material d is defined as: D d = Where D is the electric displacement and is the applied stress. Show that the potential difference generated when a stress is applied to a piezoelectric material with a dielectric constant of and width L is: V = doL (e) Piezoelectric materials can be used in lighters to generate a spark. Calculate the compressive stress that must be applied to a 5 mm thick piece of the two materials below for the resulting potential difference to be sufficient to create a spark across a 1 mm air gap: (5 marks) (3 marks) (i) Quartz where d = 300 10-12 C N1 and k=500; (4 marks) (ii) Lead zirconate titanate (PZT) where d = 400 10-10 CN-1 and K=1500. (3 marks)