Two conducting spheres of radii `r_(1)` and `r_(2)` are charged to the same surface charge density . The ratio of electric field near their surface is

Options

A. `r_(1)^(2)//r_(2)^(2)`
B. `r_(2)^(2)//r_(1)^(2)`
C. `r_(1)//r_(2)`
D. `1 : 1`

Answer

D

Explanation

As `sigma_(1) = sigma_(2)`
`:. (Q_(1))/( 4 pi r_(1)^(2)) = (Q_(2))/( 4 pi r_(2)^(2)) or (Q_(1))/( 4 pi epsilon_(0) r_(1)^(2)) = (Q_(2))/( 4 pi epsilon_(0) r_(2)^(2))`
`:. E_(1) = E_(2) or E_(1) // E_(2) = 1 rArr E : E_(2) = 1 : 1 `