Problem #7 A conducting sphere of radius a is centered on the origin. Concentric with this sphere is a conducting spherical shell of inner radius b and outer radius c. a 0 is placed on the inner sphere. Copy the figure to your own paper, and sketch in the charge density at the three surfaces at a, b, and c. (b) Use Gauss's law to determine the electric field vector for a c. Use the unit vector 7 to express your result. (c) By directly integrating - J E . di, determine the potential difference between r = a and r = b. Is the potential higher at r = a orr - b? (d) Perform another integration to determine the potential difference between r = a and a generic 7 - C. Find a numerical value of this potential difference for O - 7.0 uC, a = 4.0 cm, b = 6.0 cm, and c = 8.0 cm. Hint: The integrals will be easier if you set them up so that the lower limit corresponds to a smaller value of r. While it is possible to take the smaller r as the upper limit, this sometimes leads to a sign error if you are not very, very careful