Problem 2.7 Find the electric field a distance z from the center of a spherical surface of radius R (Fig. 2.11) that carries a uniform charge density a. Treat the case z R (outside). Express your answers in terms of the total chargec q on the sphere. [Hint: Use the law of cosines to write 2 in terms of R and 6. Be Sure to take the positive square root: NR+z -2Rz = (R-z) if R> z, but it's (z- R) if R < z.] Problem 2.8 Use your result in Prob. 2.7 to find the field inside and outside a solid sphere of radius R that carTIes a uniform volume charge density p. Express your answers in terms of the total charge of the sphere, q. Draw a graph of |E as a function of the distance from the center.