Self-Energy of a Sphere of Charge. A solid sphere of radius R contains a total charge Q distributed uniformly throughout its volume. Find the energy needed to assemble this charge by bringing infinitesimal charges from far away. This energy is called the selfenergy of the charge distribution. (Hint: After you have assembled a charge q in a sphere of radius r, how much energy would it take to add a spherical shell of thickness dr having charge dq? Then integrate to get the total energy.)

33. In a double-slit diﬀraction experiment the number of interference fringes within the central diﬀraction maximum can be increased by: A. increasing the wavelength B. decreasing the wavelength C. decreasing the slit separation D. increasing the slit width E. decreasing the slit width ans: E 34. A diﬀraction-limited laser of length ▯ and aperture diameter d generates light of wavelength λ. If the beam is directed at the surface of the Moon a distance D away, the radius of the illuminated area on the Moon is approximately: A. dD/▯ B. dD/λ C. Dλ/▯ D. Dλ/d E. ▯λ/d ans: D 35. Two stars that are close together are photographed through a telescope. The black and white ﬁlm is equally sensitive to all c