A thin, metallic, spherical shell of radius a = 4.0 cm has a charge qa = 4.00×10

Question

A thin, metallic, spherical shell of radius a = 4.0 cm has a charge qa = 4.00×10-6 C. Concentric with it is another thin, metallic, spherical shell of radius b = 9.60 cm and charge qb = 9.00×10-6 C.

Find the electric field at radial points r where r = 0.0 cm.

Find the electric field at radial points r where r = 6.8 cm.

Find the electric field at radial points r where r = 14.4 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

field at radial points r where r = 0.0 cm

as charge enclosed by a gaussian surface of radius r= 0 is zro

E = 0 N/C

electric field at radial points r where r = 6.8 cm

charge enclosed by a gaussian surface of radius r = 0.068 m is qa = 4.00×10-6 C

E = kqa/r2

substituting values we get

E = 7785467.128 N/C

electric field at radial points r where r = 14.4 cm

charge enclosed by the gaussina surface of radius r = 0.144m is qa+qb

E = k qa+qb/r2

substituting values we get

E = 5642361.111 N/C

charge on the outer surface of outer shell is equal to the sum of charges of two shells

a charge of opposite magnitude is induced on the inner surface of outer shell and total charge on the outer shell is constant by this criteria we decide tha charge on outer surface

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