Question

Problem for the following potentials, calculate Laplacis first a Tollowing potentials, calculate Laplacian first and then calculate volume density at respective points. cart (a) V= 4yz P (1,2,3) X²V=? x²+1 el (b) V= 5p² cos & P (3, Ţ; 2) - C) V= 20 (0.5, sao) om V= (A p'+ Bp") sin 4% P (05, 45,3) LOODUUUUU -oviE E Juin V = 4 al spherical condenaly) PROR 2 : Find

Answer 1

Laplacian in 6phenical Co ordinates is given by av 2 Cosd P (o5,45,6) 4 Cost 260s 73 4cost 40s0) L 4 cosd O-5 45.2548 0-0625 0 (cost) Sind) 2 -2 cosp sino cos SITO 0-0625 4 -26 1219 (o0625) REDMI NOTE 6 PRO 2548 - 26.1219 MI DUAL CAMERA ve -19.1261 Co Cchonge densly

In catesion co-0ndinats Lapacian is the iven 4yZ x1 charge density PC23) - SYZ 412 -Syz hs- - 32x L47 44 FoisSIOn's equation we Sv v-volume change densihy f 2 -3At 2n241 -49z REDMI NOTE 6 PRO 364) MI DUAL CAMERA 12 0 Sy -12 Eo

(aplacian is eyinduca co ondinales, the In iven by 1 3 2 P(3,2) sj cosd -10 cos 208 cos4 20f cosd 20cas3,,2 10 sysina -5P cosd -s 33, - 2.5 0-25 N: -15 6 Cchorge densty REDMI NOTE 6 PRO MI DUAL CAMERA