A non-uniformly charged insulating sphere has a volume charge density p that is expressed as p= Br where B is a constant, and r is the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the value for B? Sol. By definition, the volume charge density is expressed infinitesimally as p= where in is the infinitesimal charge and is the infinitesimal volume. so, we have p = dq/ = B so we can write this as dq = B dV But, dV = dr By substitution, we get the following dq = 4BT dr Using Integration operation and evaluating its limits, the equation, leads to Q = Rearranging, we get B = 4)

A non-uniformly charged insulating sphere has a volume charge density p that is expressed as p= Br where B is a constant, and r is the radius from the center of the sphere. If the, the total charge of the sphere is Q and its maximum radius is R. What is the value for B? Sol. By definition, the volume charge density is expressed infinitesimally as p= where in is the infinitesimal charge and is the infinitesimal volume. so, we have p = dq/ = B so we can write this as dq = B dV But, dV = dr By substitution, we get the following dq = 4BT dr Using Integration operation and evaluating its limits, the equation, leads to Q = Rearranging, we get B = 4)