To determine the potential of the bigger drop formed by the combination of 216 smaller drops, we need to consider the following principles of electrostatics and geometry:
1. Volume Conservation: The total volume of the bigger drop will be equal to the sum of the volumes of the 216 smaller drops. If each smaller drop has a radius
r, then the volume of one small drop is:
Vsmall=‌πr3Since there are 216 such drops, the total volume becomes:
V‌total ‌=216×‌πr3Let
R be the radius of the bigger drop. The volume of the bigger drop is:
V‌big ‌=‌πR3 By volume conservation, we have:
‌πR3=216×‌πr3or,
R3=216r3Therefore,
R=6r 2. Charge Conservation: The total charge on the bigger drop will be the sum of the charges on all the smaller drops. If each smaller drop has a potential of 200 V and radius
r, then its charge
q can be given by:
V small=‌Given
V‌small ‌=200V, we get:
q=‌For 216 such drops, the total charge
Q‌total ‌ is:
Q‌total ‌=216×‌=‌ 3. Potential of the Bigger Drop: The potential of the bigger drop can be calculated using its charge and radius. The formula for the potential of a spherical drop is:
Vbig=‌Substitute the values:
V‌big ‌=‌=‌=7200VThus, the potential of the bigger drop is 7200 V .
Answer: Option B: 7200 V