A thin, metallic, spherical shell of radius a = 6.0 cm has a charge q a = 1.00×1

Question

A thin, metallic, spherical shell of radius a = 6.0 cm has a charge qa = 1.00×10-5 C. Concentric with it is another thin, metallic, spherical shell of radius b = 10.80 cm and charge qb = 7.00×10-6 C. Find the electric field at radial points r where r = 0.0 cm.

Find the electric field at radial points r where r = 8.4 cm.

Find the electric field at radial points r where r = 16.2 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)

By Gauss Law, at r = 0.0 m, no charge is enclosed, so the electric field there is

E = 0 N/C [answer]

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b)

At r = 8.4 cm, you enclose the whole charge of ball a.

You can now treat it as a point charge by symmetry, and by Coulob's law,

E = k Qa / r^2 = 1.27*10^7 N/C [answer]

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c)

At r = 16.2 cm, you enclose the whole charge of ball a and b.

Their total charge is Qa + Qb = 1.7E-5 C.

You can now treat it as a point charge by symmetry, and by Coulob's law,

E = k (Qa + Qb) / r^2 = 5.82*10^6 N/C [answer]

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