(Solved): A cube with side lengths \( 2 a \) is centered about the origin as seen in the figure. The orange d ...

A cube with side lengths \( 2 a \) is centered about the origin as seen in the figure. The orange dot at the origin represents a point charge with charge \( Q_{\text {point }} \) The edge indicated by the green arrow has a line charge dênsity of \( \rho_{l}\left(\vec{R}_{\text {line }}\right) \). The volume enclosed by the cube has a volume charge density of \( \rho_{v}\left(\vec{R}_{v o l}\right) \) a) (3 points) Find an expression for the electric field produced by the point charge. Do not simplify the expression. b) (5 points) Find an integral expression for the electric field produced by the edge indica by the green arrow. Do not evaluate the integral. c) (5 points) Find an integral expression for the electric field produced by the volume cha density. Do not evaluate the integral. d) (2 points) Using superposition, find an expression for the electric field produced by all the charge in this problem. Do not simplify the expression.