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Concentric Spheres [12 marks]

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A solid insulating sphere of radius a = 10 cm is uniformly charged and placed at the centre of a conducting spherical shell of inner radius b = 20 cm and outer radius c = 25 cm, as shown. The electric field at a point 15 cm from the common centre is measured to be 1600 N/C directed radially inward, while the electric field at a point 50 cm from the centre is 200 V/m radially outward. From this information, find

1.: [4 marks] the net charge on the insulating sphere;
2.: [4 marks] the net charge on the hollow conducting sphere;
3.: [4 marks] the total charge on each of the inner and outer surfaces of the hollow conducting sphere.