In the figure shown

Options

A. Option1 the ratio of energy density in `I^(st)` dielectric to second dielectric is `(5)/(3)`
B. Option2 the ratio of energy density in `I^(st)` dielectric to second dielectric is `(3)/(5)`
C. Option3 total induced surface charge on the interface of the two dielectric is `(-sigma)/(6)`
D. Option4 total induced surface charge on the interface of the two dielectric is `-(2sigma)/(15)`

Explanation

(i)`(e_(1))/(e_(2))=(in_(1)E_(1)^(2))/(in_(2)E_(2)^(2))=(k_(1)E_(1)^(2))/(k_(2)E_(2)^(2))=((k_(1))/(k_(2)))((k_(1))/(k_(2)))^(2)=(k_(2))/(k_(1))=(5)/(3)`
(ii) `sigma_(B)=sigma(1-(1)/(k_(1)))-sigma(1-(1)/(k_(2)))=sigma((1)/(k_(2))-(1)/(k_(2)))=-(2sigma)/(15)`