(a) Calculate the surface charge densities on the inner( s a ) and outer( s b )

Question

(a) Calculate the surface charge densities on the inner(sa) and outer(sb) surfaces of thespherical shell.

sa = C/m2    

sb = C/m2    

(b) Calculate the net radial electric field component at thefollowing radii:

At r = 1 cm: Er = N/C    

At r = 2.5 cm: Er = N/C    

At r = 6 cm: Er = N/C    

(c) If a conducting wire is added that allows electric charge toflow between the location of q1 and theconducting shell, calculate the resulting values of the net radialcomponents of the electric fields at the following radii:

At r = 1 cm: Er' = N/C    

At r = 2.5 cm: Er' = N/C    

At r = 6 cm: Er' = N/C

Explanation / Answer

Q (inside surface of outer shell) = 3 C      induced by charge at center Q(outside surface of outer shell) = 1 C      charge left after 3 C inducedon inner surface Note that a Gaussian surface thru the outer conductor cancontain no net charge, otherwise by Gauss Law and electric field would exist and a currentwould flow in the conductor Divide by the appropriate areas to get the chargedensities b) At 1 cm E = K * (-3 C) / .012      at 2.5 cm E = 0   since noelectric field can exist within the conductor      at 6 cm   E = K * 1 C/ .062     the net charge enclosedby a Gaussian surface is 1 C c) If a wire connects q1 all of the chargewill be on the outer surface of the conductor (1 C) there can be no charge inside otherwise fields wouldexist and current would flow - Faraday's Ice Pail experiment So E = K * 1 C / .062    there can be an electric field only outside the conductor      at 2.5 cm E = 0   since noelectric field can exist within the conductor      at 6 cm   E = K * 1 C/ .062     the net charge enclosedby a Gaussian surface is 1 C c) If a wire connects q1 all of the chargewill be on the outer surface of the conductor (1 C) there can be no charge inside otherwise fields wouldexist and current would flow - Faraday's Ice Pail experiment So E = K * 1 C / .062    there can be an electric field only outside the conductor

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