A thin, metallic, spherical shell of radius a = 4.0 cm has a charge q a = 3.00×1

Question

A thin, metallic, spherical shell of radius a = 4.0 cm has a charge qa = 3.00×10-6 C. Concentric with it is another thin, metallic, spherical shell of radius b = 8.00 cm and charge qb = 6.00×10-6 C. Find the electric field at radial points r where r = 0.0 cm.

Find the electric field at radial points r where r = 6.0 cm.

Find the electric field at radial points r where r = 12.0 cm.

Discuss the criterion one would use to determine how the charges are distributed on the inner and outer surface of the shells. What is the charge on the outer surface of the outer shell?

Explanation / Answer

a = 4.0 cm,   b = 8.00 cm

qa = 3.00×10-6 C

qb = 6.00×10-6 C

A) the electric field at radial points r where r = 0.0 cm

E = 0 =======> Because r = 0 is inside the metal

B) the electric field at radial points r where r = 6.0 cm

E: a < r < b

Qen/eo = E*dA

qa/eo = E*4pi*r^2

E = qa/(4pi*eo*r^2) = (3*10^-6)/(4pi*8.85*10^-12*0.06^2) = 7.5*10^6 N/C

C) the electric field at radial points r where r = 12.0 cm

E: r > b

Qen/eo = E*dA

(qa+qb)/eo = E*4pi*r^2

E = (qa+qb)/(4pi*eo*r^2) = (9*10^-6)/(4pi*8.85*10^-12*0.12^2) = 5.6*10^6 N/C

D) charge on inner a = 0

charge on outer a = 3 x 10-6 C

charge on inner b = - cahrge on outer a = -3 x 10-6 C3 x 10-6 C

charge on outer b = charge on b - charge on inner b = 9 x 10-6 C

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