2) In left figure, lower halves of two metallic spheres of radii a = 5 mm are embedded in a dielectric with relative permittivity of & = 5. The distance between the centers of the spheres is d = 50 cm, which is much larger than the radii of the spheres. The upper half medium is air (or vacuum). The spheres are charged with charges of equal magnitudes and opposite polarities. a) Find the numerical value of the capacitance of this two-conductor system. b) If the voltage difference between the spheres is 5 Volts, calculate and express (with proper sign and unit) free and polarization charge densities where they exist. d 80 E

2) In left figure, lower halves of two metallic spheres of radii a = 5 mm are embedded in a dielectric with relative permittivity of & = 5. The distance between the centers of the spheres is d = 50 cm, which is much larger than the radii of the spheres. The upper half medium is air (or vacuum). The spheres are charged with charges of equal magnitudes and opposite polarities. a) Find the numerical value of the capacitance of this two-conductor system. b) If the voltage difference between the spheres is 5 Volts, calculate and express (with proper sign and unit) free and polarization charge densities where they exist. d 80 E