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Surface charge densities of two thin con...

Surface charge densities of two thin concentric spherical shells are `sigma` and `- sigma` respectively. Their radii are R and 2 R. Now they are connected by a thin wire.

Suppose electric field at a distance `r ( gt 2R)` was `E_(1)` before connected the two shells and `E_(2)` after connecting the two shells, then `|(E_(2))/(E_(1))|` is

A

zero

B

1

C

2

D

`.^(1)//_(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Electric field `(r gt 2R)` before connecting the shells
`E_(1)=(1xxsigmaxx4piR^(2))/(4pi in_(0)xxr^(2))+(1(-sigma)xx4piR^(2)xx4)/(4pi in_(0)xxr^(2))=sigma/in_(0)[R^(@)/r^(2)-(4R^(2))/r^(2)]`
After connecting
`E_(2)=1/(4pi in_(0))([Q_(1)-Q_(2)])/r^(2)=sigma/in_(0)[R^(2)/r^(2)-(4R^(2))/r^(2)]`
`:. E_(1)//E_(2)=1`
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