A uniformly charged solid shpere fo radius `R` has potential `V_(0)` (measured with respect to `oo`) on its surface. For this sphere the equipotentail surfaces with potentials `(3V_(0))/(2) , (5 V_(0))/(4), (3V_(0))/(4)` and `(V_(0))/(4)` have radius `R_(1), R_(2), R_(3)` and `R_(4)` respecatively. Then

Options

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

Answer

A

Explanation

We know `V_(0)=(Kq)/R=` V surface
Now `V_(i)=(Kq)/(2R^(3))(3R^(2)-r^(2))` [For `r lt R`]
At the centre of sphere `r=0`. Here `V=3/2V_(0)`
Now `5/2 (Kq)/R-(Kq)/(2R^(3))(3R^(2)-r^(2))" "R_(2)=R/(sqrt(2))`
`3/4 (Kq)/R=(Kq)/(R_(3))" "1/4(Kq)/R=(Kq)/(R_(4))`
`R_(4)=4R` Also `R_(1)=0` and `R_(2)lt(R_(4)-R_(3))`