Download ph504-1011-ass1 - University of Kent

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.