1) An insulating sphere with radius R has a uniform positivevolume charge density of ρ. A solid metallic shell with innerradius R and outer radius 2R has zero total charge. [Express youranswers for parts (a-d) using ρ, R, and constants]

(a) What is the magnitude of the electric field at a distance ?= 3? away from the center?

(b) Assuming the potential at infinity is 0. What is thepotential at the outer surface (? = 2?) of the metallic shell?

(c) What is the potential at the inner surface (? = ?) of themetallic shell?

(d) What is the potential at the center of the insulating sphere(? = 0)?

(e) If the metallic shell is replaced with an insulating shellwith inner radius R and outer radius 2R that has no chargeanywhere. The insulating core remains the same. Circle below whichone(s) of the previous questions will have a different answer? a.b. c. d.

(f) Two long straight parallel conductors are a distance 4?apart center-to-center. A thin-walled cylindrical shell with itscenter at ? = 0 has radius ? and carries a current 3? along the +?direction. A wire at ? = 4? carries a current ? also along the +?direction. What is the magnitude of the magnetic field at ? = 2??[Express your answers using ?, ?, and constants]

(g) Find the coordinate of the location on the ?-axis where thetotal magnetic field is 0. [Express your answers using ?, ?, andconstants]