Two concentric conducting thin shells of radius R and 2 R carry charges +Q and +3Q respectively. The magnitude of electric field at a distance x outside and inside from the surface of outer sphere is same. Then the value of x is

Options

A. `R/3`
B. `(2R)/3`
C. `R/4`
D. `R/2`

Answer

B

Explanation

Electric field at a distance x outside from surface of outer shell `=1/(4piepsilon_(0))(Q+3Q)/((2R+x)^(2))`
Electric field at a distance x inside from surface of outer shell `=1/(4piepsilon_(0)) Q/((2R-x)^(2))`
`:. 1/(4piepsilon_(0)) (4Q)/((2R+x)^(2))=1/(4piepsilon_(0)) Q/((2R-x)^(2))`
`rArr x=(2R)/3`