P3. In a hydrogen atom in its lowest energy state (known as the ground state), the electron forms a spherically-symmetric "cloud" around the nucleus, with a charge density given by p = A exp(-2r/a.), where a, = 0.529 A = 0.529 x 10 " m is the Bohr radius. (a) Determine the constant A. (b) What is the electric field at the Bohr radius? P4. A charged sphere of radius R has a non-uniform charge distribution given by Po 1 - 6* where b = 0.98, R = 2.50 cm, and p, = 1.05 pC/m'. Plot the electric field from r = 0 to r = 3R. P5. A very long thin rod creates an electric field of magnitude E =1.35 kN/c at a distance 3.25 cm from it. How much charge is on a 10.0-cm segment of this rod? P6. A very long cylinder of radius a = 1.00 cm has a uniform charge density +15.0 nC/cm'. It is surrounded by a very long concentric uniformly-charged hollow cylinder of inner radius b = 3.00 cm and outer radius c = 4.00 cm. If the electric field is measured to be zero at a distance r = 6.00 cm from the common axis of these two cylinders, calculate the charge density in the hollow cylinder. P7. Two large thin sheets of charge have equal but opposite surface charge densities. (a) Determine the electric field between these sheets. (b) Determine the electric field outside of these sheets P8. Suppose a neutral spherical conducting shell has an inner radius of 10.0 cm and an outer radius of 15.0 cm. A charge of +4.50 pC is placed at the center of the shell. Calculate the charge densities on the inner and outer surfaces of the shell. P9.(a) A cylindrical conducting tube has a net charge of +3.7 aC per meter of length. The tube has an inner radius of 1.9 cm and an outer radius of 2.3 cm. Determine the charge densities on the inner and outer surfaces of the tube. (b) A long line of charge with A = -2.3 AC/m is placed at the center of the tube. Calculate the new charge densities on the inner and outer surfaces of the tube. P10.(a) A neutral spherical conducting shell of inner radius 12 cm and outer radius 15 cm has a charge of -3.9 nC placed inside (but not at the center). Compute all of the following that can be determined. If the quantity cannot be determined, explain why. (a) The charge on the inner surface. (b) The charge density on the inner surface. (c) The charge on the outer surface. (d) The charge density on the outer surface