The electrostatic potential inside a charged sphere is given as V=A r^2+B , where r is the distance from the centre of the sphere, A and B are constants. Then, the charge density in the sphere is

Step-by-step solution

Let the volume charge density be . The electric field inside the charged sphere, E= K q r R^3 where, R= Radius of charged sphere r= Distance of the point (P) inside the sphere As volume charge density is , then in terms of charge density, aligned E & = r 3 ₀ & = 3 E ₀ r aligned Now, electric field, E=- d V d r Here, V=A r^2+B array ll & E=- d V d r =-2 A r+0=-2 A r & = 3 E ₀ r array = 3 (-2 A r ₀ ) r =-6 A ₀