(Solved): A nonuniform, but spherically symmetric, distribution of charge has a charge density \( \rho(r) \) ...

A nonuniform, but spherically symmetric, distribution of charge has a charge density \( \rho(r) \) given as follows: \( \begin{array}{lll}\rho(r)=\rho_{0}(1-r / R) & \text { for } r \leq R & \text { Find the value of } r \text { at which the electric field is maximum. } \\ \rho(r)=0 & \text { for } r \geq R & \text { Express your answer in terms of some or all of the variables } r, R, Q \text {, and appropriate constants. } \\ \text { where } \rho_{0}=3 Q / \pi R^{3} \text { is a positive constant. } & \end{array} \) where \( \rho_{0}=3 Q / \pi R^{3} \) is a positive constant. Part E Find the value of that maximum field. Express your answer in terms of some or all of the variables \( r, R, Q \), and appropriate constants.