Eight small drops, each of radius r and having same charge q are combined to form a big drop. The ratio between the potential of the bigger drop and the potential of the smaller drop is

Question

Eight small drops, each of radius r and having same charge q are combined to form a big drop. The ratio between the potential of the bigger drop and the potential of the smaller drop is (A) 8: 1 (B) 4: 1 (C) 2: 1 (D) 1: 8

Tardigrade Admin · Accepted Answer

Radius of bigger drop (8)1/3 r = 2r. Total charge = 8q. Potential of bigger drop = 8q/4π ε0 R = 8 q/ 4 π ε0 (2r) = 4 [q/4 π ε0 r] = 4 times the potential of single drop.

Q. Eight small drops, each of radius $r$ and having same charge $q$ are combined to form a big drop. The ratio between the potential of the bigger drop and the potential of the smaller drop is

8 : 1

4 : 1

2 : 1

1 : 8

Radius of bigger drop $(8)^{1/3} r = 2 r$ . Total charge = $8 q$ . Potential of bigger drop = $8_{q} /4 π ε_{0} R = 8 q /4 π ε_{0} (2 r) = 4 [q /4 π ε_{0} r]$ = 4 times the potential of single drop.

Q. Eight small drops, each of radius r and having same charge q are combined to form a big drop. The ratio between the potential of the bigger drop and the potential of the smaller drop is