Question

a metal Spherical ith vadus R has a dense distribution of chorge van which changes with r by the equation p or, with o Cons ton andtradia t Rositi on inside the ali the Pr the beundary conditions as Tollous in (r R) eauation 'u with ui is the elecwostate potential in the sphere ω{th the trundar7 condition Out side theGphere (r>R) the laplace eauation ue-Owieh Uo is the electrostatic prential cutside the sphere with the wundary conditionand for arpties o (e)Ci (P) Speci f γυί,Ui (r ) (ngde the çnae and uo,Uo(r) cuteidlehlephere using the boundary condition ro ,es i Co) o Lo

Answer 1

Dishibulion o chatge is given t C eleehefeld aļaese gegions Then ^eq/ons e Can ind Eleelnic -ßelol inside using Causs lai I51 "j.dy sine de d4 → Due 10 2X So Gaussian Suvface hele, avea 47

enel 2 From Coauss lacJ Cu od

IR グ 12 Eo 一 R. dR 12 Eo l22o αγ 3 3 3 1つ 12 Eo