NEETPhysicsElectrostatics
N identical spherical liquid drops, each charged to the same potential, coalesce to form a single large drop. Match the physical quantities of the large drop in List-I with their scaling factor relative to a single small drop in List-II. List-I List-II (A) Capacitance (I) N^ 5/3 (B) Electric potential (II) N (C) Total electrostatic energy (III) N^ 1/3 (D) Total charge (IV) N^ 2/3 Choose the correct answer from the op
Options
- A(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
- B(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
- C(A)-(III), (B)-(IV), (C)-(II), (D)-(I)
- D(A)-(IV), (B)-(I), (C)-(II), (D)-(III)
Correct answer
B. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
Step-by-step solution
Let the radius of a single small drop be r , its charge be q , and its capacitance be c . When N drops coalesce, the volume is conserved: 4 3 R^3 = N ( 4 3 r^3 ) R = N^ 1/3 r (A) Capacitance of a spherical conductor is proportional to its radius ( C = 4 ₀ R ). C = N^ 1/3 c . Scaling factor is N^ 1/3 . (D) Total charge is conserved: Q = Nq . Scaling factor is N . (B) Electric potential V = 1 4 ₀ Q R V Nq N^ 1/3 r = N^ 2/3 v . Scaling factor is N^ 2/3 . (C) Total electrostatic energy U = 1 2 QV U (Nq)(N^ 2/3 v) = N^