1) An insulating sphere with radius R has a uniform positive volume charge density of p. A solid metallic shell with inner radius R and outer radius 2R has zero total charge. [Express your answers for parts (a-d) using P, R, and constants) 2R conductor R (a) (2 pts) What is the magnitude of the electric field at a distance r = 3R away from the center? insulator (b) (3 pts) Assuming the potential at infinity is 0. What is the potential at the outer surface (r = 2R) of the metallic shell? (c) (3 pts) What is the potential at the inner surface (r = R) of the metallic shell? (d) (6 pts) What is the potential at the center of the insulating sphere (r = 0)? 2R insulator (e) (4 pts) If the metallic shell is replaced with an insulating shell with inner radius R and outer radius 2R that has no charge anywhere. The insulating core remains the same. Circle below which one(s) of the previous questions will have a different answer? a. b. d. R c. insulator (f) (6 pts) Two long straight parallel conductors are a distance 4R apart center-to-center. A thin-walled cylindrical shell with its center at x = 0 has radius R and carries a current 3i along the +z direction. A wire at x = 4R carries a current i also along the +z direction. What is the magnitude of the magnetic field at x = 2R? (Express your answers using R, i, and constants] y 3i 0 R 4R (out of page) (g) (6 pts) Find the coordinate of the location on the x-axis where the total magnetic field is 0. [Express your answers using R, i, and constants)
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