Question

4. A chemical engineer is designing a sensor system and needs to know the energy of inter- action of two water molecules. The diagram below shows two water molecules separated by a distance 2d in the x - y plane with x in the horizontal direction. The origin of coordinates is at the water molecule on the left. Large arrows show the directions of the dipole moment vectors of the two water molecules. The magnitude of the intrinsic electric dipole of a single water molecule is p = 6.2 × 10-31 cm 2 (a) Evaluate the r and y components of the dipole vector of the water molecule on the left side. (2 marks) (b) Given that, at a location r, the electric potential of a pure dipole of dipole moment p located at the origin is V(r) show that at the location (2d, y) the electric potential caused by the left dipole in the diagram is 1 py in the limit that y2. (3 marks) (c) From the potential in (b) find an expression for the electric field vector E, giving both of its components, caused by the water molecule on the left at the location of the water molecule on the right. Then evaluate the field for d -5 nm. (3 marks) (d) Find the total energy of the system of two dipoles for d = 5 nm. (2 marks)

Answer 1

(o,0) (o p) -31

ft HRE. ft @d)3 ved,d) ー一4자 = 3AT6 c) ret,

つ乂 Rpxt 1311 4짜 No-uD