Question 687: Electrostatics & Capacitance

Question

512 identical drops of mercury are charged to a potential of 2V each. The drops are joined to form a single drop. The potential of this drop is ________ V.

Accepted Answer

Let charge on each drop = q
radius = r
$$v = {{kq} \over r}$$
$$ \Rightarrow $$ $$2 = {{kq} \over r}$$
radius of bigger
$${4 \over 3}\pi {R^3} = 512 	imes {4 \over 3}\pi {r^3}$$
$$R = 8r$$
$$ 	herefore $$ $$v = {{k(512)q} \over R} = {{512} \over 8}{{kq} \over r} = {{512} \over 8} 	imes 2$$
$$ = 128V$$

Electrostatics & Capacitance

512 identical drops of mercury are charged to a potential of 2V each. The drops are joined to form a single drop. The potential of this drop is ________ V.

Integer / Numeric Answer Type