A very long, solid cylinder with radius R has positive chargeuniformly distributed throughout it, with charge per unit volume r.(a) Derive the expression for the electric field inside the volume at adistance r from the axis of the cylinder in terms of the charge density r.(b) What is the electric field at a point outside the volume in terms ofthe charge per unit length l in the cylinder? (c) Compare the answers toparts (a) and (b) for r = R. (d) Graph the electric-field magnitude as afunction of r from r = 0 to r = 3R.

An infinitely long nonconducting cylinder of radius R and carrying a nonuniform volumecharge density of ρ(r) = ar where a is a constant.(a) Calculate charge per unit length of the cylinder (b) Find the expressions for the electric field due to this charged cylinder. You should find oneexpression for the electric field in the region r < R and a second expression for the field in theregion r > R

In Figure (a) below, a particle of charge +Q produces an electric field of magnitude Epart at point P, at distance R from the particle. In Figure (b), that same amount of charge is spread uniformly along a circular arc that has radius R and subtends an angle 8. The charge on the arc produces an electric field of magnitude Earc at its center of curvature P. For what value of 0 (in º) does Earc = 0.75Epart? (Hint: You will probably resort to a graphical solution.) +Q |▬▬▬R—-|| Number i P (a) AR +Q}/0/2/ (b) Units ° (degree: