The electrostatic potential inside a charged spherical ball is given by V=a r^2+ b where ' r ' is the distance from its centre and ' a ' and ' b ' are constants. The volume charge density of the ball is [ ₀= . permittivity of free space]

Step-by-step solution

Given: V=a^2+b Given : V = ar ^2+ b aligned E & =- d V d r & =- d d r (a r^2+b ) E & =-2 a r ...(i) aligned By Gauss' law, E ~S = q ₀ 4 r^2 E= q ₀ ...(ii) Total charge (q) enclosed = 4 p 3 r^3 . From (i) and (ii) ( = charge density of ball ) aligned & 4 r ^2 (-2 ar )= 4 3 ₀ r ^3 & -2 a = 3 ₀ aligned =-6 a ₀