Point P is distance 2R from the center of an extremely long uniform cylinder of radius R. Only a finite length of the cylinder is drawn above. The cylinder is solid, and has an unknown uniform charge per unit volume, a density we can call p. Point Q is on the interior of the cylinder at distance R/3 from the center. ▪ (a) If the electric field at point P at distance 2R is found to be radially inward and of given size Ep, find the charge density p. Is p positive or negative? Given an expression in terms of R, Ep and Eo. ■ (b) Find the size EQ of the electric field at point Q, a distance R/3 from the center. Is the field there radially inward or outward? Please solve both parts using Gauss's Law, indicating your choices for Gaussian surfaces with a drawing and word or two.

Point P is distance 2R from the center of an extremely long uniform cylinder of radius R. Only a finite length of the cylinder is drawn above. The cylinder is solid, and has an unknown uniform charge per unit volume, a density we can call p. Point Q is on the interior of the cylinder at distance R/3 from the center. ▪ (a) If the electric field at point P at distance 2R is found to be radially inward and of given size Ep, find the charge density p. Is p positive or negative? Given an expression in terms of R, Ep and Eo. ■ (b) Find the size EQ of the electric field at point Q, a distance R/3 from the center. Is the field there radially inward or outward? Please solve both parts using Gauss's Law, indicating your choices for Gaussian surfaces with a drawing and word or two.