! Problem 2.5 Find the electric field a distance z above the center of a circular loop of radius r (Fig. 2.9) that carries a uniform line charge A. Problem 2.6 Find the electric field a distance z above the center of a flat circular disk of radius R (Fig. 2.10) that carries a uniform surface charge σ. What does your formula give in the limit R oo? Also check the case z » R. 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 σ. Treat the case z < R (inside) as well as z> R (outside). Express your answers in terms of the total charge q on the sphere. [Hint: Use the law of cosines to write 2 in terms of R and 0. Be sure to take the positive square root: R2+z2-2Rz = (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 carries 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.