The electric field along the axis of a uniformly charged disk of radius R and total charge Q was calculated in Example 23.9. Show that the electric field at distances x that are large compared with R approaches that of a particle with charge Q 5 spR2. Suggestion: First show that x/(x 2 1 R2)1/2 5 (1 1 R2/x 2)21/2 and use the binomial expansion (1 1 d)n < 1 1 nd, when d ,, 1.
Chapter4:Two-DimensionalKinematics Ittakes1numbertospecifyapositionona1-dimensionalline,2numbers fora2-dimensionalspace,and3numbersfora3-dimensionalspace. Tocreateacoordinatesystemin2-dimensionstakeapointattheoriginand definetwoperpendiculardirectionstoorientthesystem. *curlynotaionwithmagnitudeanddirectionasthetwonumber s;itispolar planesystem Paraenthesisnotationwithtwonumbersascompoents;Cartesian coordinates. Anythingmovingalongacurvedpathhasaninstantaneousvelocityvector whosedirectionistangenttothecurve,ateachpoint ofthepath,andwhose magnitufeistheinstantaneousspeedoftheobjectalongthepath. Accelerationistherateofchangeofvelocity,notspeed. -accelerationincludesc