Consider two spherical infinitely thin conducting surfaces (= ∞o) with the same center. The cross section of this configuration is shown below. The inner sphere (radius a) has a total negative charge of -Q. The outer sphere (radius b) has a positive charge with unknown amount. Assume the electric potential at the center is Vo (Vo > 0) and at infinity is zero. Also, assume free-space permittivity in all regions. (a) Find the electric potential V(R) at the distance R from the center for 0 < R < b. (b) Find the amount of positive charge on the outer sphere. Hint: The integral form of Gauss' Law is your best friend! Also you may pay close attention to the net charge.

Consider two spherical infinitely thin conducting surfaces (= ∞o) with the same center. The cross section of this configuration is shown below. The inner sphere (radius a) has a total negative charge of -Q. The outer sphere (radius b) has a positive charge with unknown amount. Assume the electric potential at the center is Vo (Vo > 0) and at infinity is zero. Also, assume free-space permittivity in all regions. (a) Find the electric potential V(R) at the distance R from the center for 0 < R < b. (b) Find the amount of positive charge on the outer sphere. Hint: The integral form of Gauss' Law is your best friend! Also you may pay close attention to the net charge.