NEETPhysicsElectrostatics
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): When N identical charged liquid drops coalesce to form a single large drop, the surface charge density of the large drop is strictly greater than that of a single small drop. Reason (R): During coalescence, the total charge remains conserved while the total surface area of the system increases. In
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- C(A) is true but (R) is false
- D(A) is false but (R) is true
Correct answer
C. (A) is true but (R) is false
Step-by-step solution
Assertion (A) is true: Let the radius of a small drop be r and its charge be q . Its surface charge density is = q 4 r^2 . When N drops coalesce, the new radius is R = N^ 1/3 r and the new charge is Q = Nq . The new surface charge density is ' = Q 4 R^2 = Nq 4 (N^ 1/3 r)^2 = N^ 1/3 . Since N > 1 , we have ' > . Thus, the surface charge density increases. Reason (R) is false: While the total charge is conserved, the total surface area of the system decreases. The initial total surface area is N(4 r^2) , and the fina