Question

Question 11: Can you calculate the electric field of a dipole using Gauss' Law? If yes, sketch the Gaussian surface you would use. If no, explain why not, including a sketch. 3 Using Gauss' Law to calculate the electric field of a spherical object Question 12: a) What is the volume charge density p= for a uniformly charged solid sphere of radius R and with total charge Q? Sketch a graph of p as a function of radius, r; mark the radius R in your graph.

Answer 1

11 we cannot alculate electric feild of di pole using (Actassen Gauss' Law Be cause in Gauss' low we consider a closed surface can equipotential surface) to find Ê over that closed surface, we Eslate equite surface integral of E with total charge enclosed the surface Etimes. The Eo) et ie gedse toti charge Eo since is the case of Dipole (equat have (dipole have equal and oposite charge) there for total charge enclosed in the surface (tq-q=o) equels zere le $6.03 -0,; but electric feild due to a diple

Cannot be zero. Ten v an - Consider a around Gerassian clipole Surface cand man < Cylindrical Grausing surfall tatal charge/ total flux Shaph the surface = Zero

3) Consider a solid sphere havine Volume chaye density 8-% Radius, R We need to find Ê and inside the sphere 2 outside the sphere. @ inside the sphere , En tot for that consider a Gaussine Surface inside (Spherical surface) inside the solid sphere having a radius X . by applying Gauss' law, § E ds = 1 / 6x charge enclosed in it chage enclosed, Genc = Sx Venclosed

Rene ² 8x4/35 x ² & E. d3 = 48 4x² Ein fods = 1, 34/ 3 ² Ein A x² = 1, 84/ 23 EO To 3 - Electric feild inside the sphere at a distance ☆ buc ® for Get the outside The sphere, so nhile Considery out sicle the sphere total charge deu z fx 47 R² enclosed Gene 3x "R t Galessian Surface.

whe fe ds = ,437R3x8 Ē. 419 r?= Y, 4/3 TR3S E dge when Q = Vyveis E te me for YOR Es x for XLR 4 &O 12 1. total change 12) for a uniformly changed solid sphere, Radius-R, & total charge ca. The Yolume chaye density, sza 42TR3 radius & Sahate since 8 is independ of radius, it is constant anywhere in sphere.