A thin nonconducting spherical shell of radius R 1 carries a total charge q 1 th

Question

A thin nonconducting spherical shell of radius R1 carries a total charge q1 that is uniformly distributed on its surface. A second, larger thin non-conducting spherical shell of radius R2 that is concentric with the first carries a charge q2 that is uniformly distributed on its surface.

q1 q2 A thin nonconducting spherical shell of radius R1 carries a total charge q1 that is uniformly distributed on its surface. A second, larger thin non-conducting spherical shell of radius R2 that is concentric with the first carries a charge q2 that is uniformly distributed on its surface. (a) Use Gauss's law to find the electric field in the regions r

Explanation / Answer

Given the two spherical shells are non conductors

Electric field at r < R1 constust a gaussian surface with this radius inside the sherical shell

inside the sperical shell the charge enclosed Q =0

Accrording to gauss law

electric flux E (4?r^2 ) = Q / ?_0 == > E = kQ /r^2

since Q =0

E (r<R1) = 0

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The electric field at a point E (R1 < r < R2 )

Electric field at R1 < r < R2 constust a gaussian surface with this radius

Electric field at this point E = Eshell (R1) + Eshell (R2)

The electric field due to Eshell (R2) = o , since the point is inside the outer shell

Eshell (R1) = kq1 / r^2

Electric field (R1 < r < R2 ) = kq1 / r^2 + 0 = kq1 / r^2

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The electric field at a distace r > R2 outside the outer spherical shell

Electric field E = Eshell (R1) + Eshell (R2)

electric field due to inner shell

Eshell (R1) = kq1 /r^2

electric field due to outer shell

Eshell (R2) = kq2 /r^2

E (r > R2) = kq1 /r^2 + kq2 /r^2

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The ratio of charges must be q1 / q2 = -1 then E (r > R2) = 0

q1 = + ve and q2 = -ve (OR) q1 = - ve and q2 = +ve

either of two cases E (r > R2) = 0

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