Question 20: Electrostatics & Capacitance

Question

The potential of a large liquid drop when eight liquid drops are combined is 20 V , then the potential of each single drop was

Accepted Answer

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:
$    \left(\frac{4}{3} \pi r^3ight) 	imes 8 = \frac{4}{3} \pi R^3    $
Simplifying gives:
$    2r = R \quad \ldots 	ext{(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 \quad \ldots 	ext{(ii)}    $
Potential Derivation:
The potential for one small drop ($ V' $) and the large drop ($ V $) are given by:
$    V' = \frac{q}{4 \pi \varepsilon_0 r}    $
$    V = \frac{Q}{4 \pi \varepsilon_0 R}    $
Finding the Ratio:
Using the above expressions, we derive:
$    \frac{V'}{V} = \frac{q}{Q} 	imes \frac{R}{r}    $
Substituting from equations (i) and (ii), we get:
$    \frac{V'}{20} = \frac{q}{8q} 	imes \frac{2r}{r}    $
This simplifies to:
$    \frac{V'}{20} = \frac{1}{4}    $
Calculating $ V' $:
Solving for $ V' $, we find:
$    V' = 5 \, 	ext{V}    $
Thus, the potential of each single small liquid drop is 5 V.

Answer

10 V

Answer

7.5 V

Answer

5 V

Answer

2.5 V

Electrostatics & Capacitance

The potential of a large liquid drop when eight liquid drops are combined is 20 V , then the potential of each single drop was

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