Question 726: Electrostats & Capacitance

Question

64 identical drops each charged upto potential of $$10 ~\mathrm{mV}$$ are combined to form a bigger drop. The potential of the bigger drop will be __________ $$\mathrm{mV}$$.

Accepted Answer

The problem involves 64 identical drops, each charged up to a potential of $$10 \mathrm{~mV}$$, that are combined to form a bigger drop. We are asked to find the potential of the bigger drop.
The potential of each drop is given by:
$$V = \frac{Kq}{r}$$
where $$K$$ is the Coulomb constant, $$q$$ is the charge on each drop, and $$r$$ is the radius of each drop.
The radius of the bigger drop is:
$$R = 4r$$
since the 64 identical drops combine to form a bigger drop.
The total charge on the 64 identical drops is:
$$Q = 64q$$
The potential of the bigger drop is:
$$V_{bigger} = \frac{KQ}{R} = \frac{K(64q)}{4r} = 16 \frac{Kq}{r} = 16V = 16 	imes 10 \mathrm{~mV} = 160 \mathrm{~mV}$$
Therefore, the potential of the bigger drop is $$160 \mathrm{~mV}$$.

Electrostats & Capacitance

64 identical drops each charged upto potential of $10 ~\mathrm{mV} are combined to form a bigger drop. The potential of the bigger drop will be __________ \mathrm{mV}$.

Choose the correct answer: