Question

Find the field inside and outside a sphere of radius R, which carries a volume charge density purpo. Find Qenclosed for a Gaussian shape inside and outside the charge distribution. Find SE da for a Gaussian shape inside and outside the charge distribution.

Answer 1

I have explained thoroughly. Please feel free to ask me if any confusion arises regarding this.

Volume charge deneily 8=850 Inside the sphere We are to find the electric field at any internal point o at a distance r. We consider a Gaussian surface which is a concatrie sphere passing through P in this case. According to Eids - Qenc (Gauss's law) - 1 / 6 / 8(x) uradx Given f (x) = xLo : E (478²) = 1/2 (sox (4x²) da - Toxun sada E (UTY") - MOTO Y E = A x uz * -

E r² So E. - this is the electric field at an à point inside the sphere at a distance 8 (4R) from the centre. Outside the sphere Sphone Total charge as within the Q = se dv = S(re.) ² sine do dodr - Utto (.r3d8 - TISOR" 0 OR (rse OK The electric field at p at a distance & (>R) is- E (Eds = 16 Qene. Elds - TISOR E (48²) = TITORY /

outside the So electric field sphere E - I L P So, shape Q enclosed inside for the a Gaussian charge distribution & and D outside Qene - TIR' SE.da for a Gaussian shape inside the charge distribution - 15.00 the change Outside distribution = ITTO RY Final Inde Result Inside Outside - - Electric field 825./6o Sollubor2