Question

- Sphere filled with charge - Consider a sphere with radius a. It is filled with charge of constant density s cims. Find the electric field outside and inside me sphere.

Answer 1

Electric Field Outside and Inside the Sphere of radius a can be calculate by

Gauss Law in Electrostatics

Given, radius of Sphere = a charge of Constant density =P / m3 Electric field outside the sphere = ? Electric field inside the sphere = ? In the problem it is given charge of Constant density". This means Toral charge is distributed uniformely through out the sphere, so here sphere is called "Non-conducting sphere". chaye density, s = 9 = Constant That men charge for unit volume constant. Let a charge aj is distributed uniformely through out the volume of sphere. Electric field outside the sphere To solve Electric field of the sphere inside or outside we have to ure of "Gauss low" Gauss low says that, $ 2.da a 0 E= Electric field ..JA = Area vector a inside = change inside the closed area or inside the Gaussian Surface to = permitivity of tree space.

64 Sphere Gaussian spher To solve Gauss lw we have to amune a Geussian surface which meense of any shape is sphere, cylinder To find Electric field outside the sphere assume a point outside the sphere I at a distances from ! Center of splue. Now drow a aussian sphere with this radius r. At s' Eletric filed (E), Area (da) are in same direction. hence . Enda Gela como - Eda Cosó e EdA From Equation ③ we get & Eida = vinside $ Eda coso = 1 / 4 Vinside = a. ) Total chare a present geda - en inside the Gaussian splure t. 6 da = a do . CE = content] F(A) - E (A) = PV ES===$v] Exfurface Area of) = L Volume of sphere) Kaussian sphere to EA)

Ex(488) *PRAZ ET EXB Xarxedot Electric field outside the sphere a= radius of Sphere E = 36. Lyn) Y= raclius of Ganesian - sphere Electric field inside the sphere To find theetric field inside the sphure Assume a point inside at a distancer from Center of the sphere and also draw a Gaussian sphure with this radius r. Here we don't know how muth cheye is present inside the Gaussian Sphere. so let Winside = q = Sv 1. r= volume of Gaussian sphere of qution according to Gauss law & Edă = avinside

$ Edaloso' al sedaco - Leve E & da = V (?e=Gusta) . E (A) = full av - sphere Gaussian sphere C E Ex (137) - Page x 4 *y*x 62- =falt). Larios Inside the sphere, Electric tiled Electric out side tiend the sphere, out side the sphere, even they E = 3 Electric inside tired the sphere, Greaph: outside Inside EXY