A solid metal sphere of radius a = 1.30 cm is surrounded by a concentric spheric

Question

A solid metal sphere of radius a = 1.30 cm is surrounded by a concentric spherical metal shell of inner radius b = 3.00 cm and outer radius c = 3.50 cm. The inner sphere has a net charge of Q1 = 3.50 µC, and the outer spherical shell has a net charge of Q2 = -8.40 µC.

What is the radial component of the electric field Er at a point located at radius r = 2.70 cm, i.e. between the two conductors? Er is positive if it points outward, negative if it points inward.

What is Er at a point located at radius r = 3.90 cm, i.e. outside the outer shell?

What is the surface charge density, sb, on the inner surface of the outer spherical conductor?

What is the surface charge density, sc, on the outer surface of the outer spherical conductor?

Explanation / Answer

Q1 = 3.5 uC all charge on surface of sphere Q2i = -3.5 uC induced by charge on sphere (inner surface of shell) Q2o = -8.4 - (-3.5) = -4.9 uC left on outer surface of shell Q2o is also the net charge on the system. Divide by appropriate surface areas to get surface charge density. Er (between conductors) = k Q1 / .027^2 Er (outside conductors) = k Q2o / .039^2 due to net charge E fields are directed away from + charges and towards - charges. Substitute and solve where k = 9 * 10E9 and units are in meters and coulombs.

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