If N drops of same size each having the same charge, coalesce to form a bigger drop How will - Physics - Electrostatic Potential And Capacitance

Question

If N drops of same size each having the same charge, coalesce to
form a bigger drop How will the following vary with respect to
single small drop? (3) (i) Total charge on bigger drop (ii)
Potential on the bigger drop (iii) Capacitance

Ujjval Chauhan · Accepted Answer

Dear student

Let r,q and v be the radius, charge and potetial of a small drop
 The total charge on the bigger drop is the sum of all charge on small drops sQ=Nq The volume of N small drops=N×43πr3and for the bigger drop =43πR3hence 43πR3= N×43πr3R=N1/3rso the potential on bigger dropV=14πεoQR=14πεoNqN1/3r=N2/3×14πεoqrV=N2/3×vand the capacitance    C=4πεoRC=4πεoN1/3r=N1/34πεorC=N1/3c

If N drops of same size each having the same charge, coalesce to form a bigger drop. How will the following vary with respect to single small drop? (3) (i) Total charge on bigger drop (ii) Potential on the bigger drop (iii) Capacitance