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PH504/10/01 UNIVERSITY OF KENT SCHOOL OF PHYSICAL SCIENCES 2010/11 Assignment 1: Analysis 1. Calculate the gradient () of the following functions (assume Cartesian co-ordinates) (a) 2x3+2y2+z2, (b) exy, (c) 4 sin(xyz) . 2. Two positive point charges are a distance r apart. The total charge of the pair is Q. If each charge is Q/2, the force of repulsion is F0 . a. Show that the force can never be greater than F0 no matter how the total charge is divided. b. What are the two charges if the force is 3/4F0 ? 3. A surface charge density (x,y) is given by (x,y)=3x2+4y2-xy Cm-2. Calculate the total charge contained within the area bounded by x=0+a, y=0+a. Your answers should be easily legible and carry with them an explanation of the steps taken. Deadline: Friday, Week 2, 11:55am , only to be handed in directly to me.