When eight small liquid drops combine to form one large drop, the potential of the large drop is given as 20 V . We need to find the potential of each individual small drop.
Solution
Volume Relationship:
The total volume of the eight small drops is equal to the volume of the one large drop. This relationship is expressed as:
(‌πr3)×8=‌πR3Simplifying gives:
2r=R‌‌...‌ (i) ‌This equation indicates the radius of the large drop
R is twice the radius of one small drop
r.
Charge Conservation:
The total charge of the eight small drops is equal to the charge of the large drop:
8q=Q‌‌...‌ (ii) ‌Potential Derivation:
The potential for one small drop
(V′) and the large drop
(V) are given by:
‌V′=‌‌V=‌Finding the Ratio:
Using the above expressions, we derive:
‌=‌×‌Substituting from equations (i) and (ii), we get:
‌=‌×‌This simplifies to:
‌=‌Calculating
V′ :
Solving for
V′, we find:
V′=5vThus, the potential of each single small liquid drop is 5 V .