Plot a graph comparing the variation of potential ‘V’ and electric field ‘E’ due to a point charge ‘Q’ as a function of distance r from point charge
(ii) Find the ratio of the potential differences that must be applied across the parallel and the series combination of two identical capacitors so that the energy stored, in the two cases, becomes the same.

Explanation

(i) The graph variation of potential and electric field due to a point charge Q with distance R fro the point charge is shown in figure.
(ii) Let C be capacitance of each capacitor.
In series arrangement net caapcitance `C_(S)=(C)/(2)`.
In parallel arrangement, net capacitance, `C_(P)=2C`
Energy stored `U=(1)/(2)CV^(2)`
If `V_(S) and V_(p)` are potential difference applied across series parallel arrangments, then given
`U_(S)=U_(p) implies (1)/(2) C_(S)V_(S)^(2)=(1)/(2)C_(p)V_(p)^(2) implies (V_p)/(V_(S))=sqrt((C_(S))/(C_(p)))=sqrt((C//2)/(2C))=(1)/(2)`