त्रिज्या R के किसी एक समान आवेशित ठोस गोले के पृष्ठ का विभव `V_(0)` है | (`oo` के सापेक्ष मापा गया ) | इस गोले के लिये, `(3V_(0))/(2), (5V_(0))/(2), (3V_(0))/(4),` तथा `(V_(0))/(2)` विभवों वाले समविभवी पृष्ठों की त्रिज्यायें क्रमशः `R_(1), R_(2), R_(3)` तथा `R_(4)` है | तो

Options

A. `R_(1)=0` तथा `R_(2) gt (R_(4)-R_(3))`
B. `R_(1) ne 0` तथा `(R_(2)-R_(1)) gt (R_(4)-R_(3))`
C. `R_(1)=0` तथा `R_(2) lt (R_(4)-R_(3))`
D. `2R lt R_(4)`

Answer

C, D

Explanation

`V_(0)=(KQ)/(R )`
`V_((rgtR))=(KQ)/(r)`
`V_((rlt R))=(KQ)/(2R^(3))(3R^(2)-r^(2))`
`V_("centre")=(3)/(2)(KQ)/(R )=(3V_(0))/(2 )`
`R_(2)` पर `V=(5V_(0))/(4)=(kQ)/(2R^(3))(3R^(2)-R_(2)^(2))`
`rArr (5)/(2)=3-(R_(2)^(2))/(R ) rArr R_(2)=(R )/(sqrt2)`
`R_(3)` पर `V=(3V_(0))/(4)=(kQ)/(R^(3)) rArr R_(3)=(4)/(3)R`
`R_(4)` पर `V=(V_(0))/(4)=(kQ)/(R_(4)) rArr R_(4)=4R`
`therefore R_(4)-R_(3)=4R-(4)/(3)R=(8R)/(3) gt R_(2)`