First slide
Charges
Question

A small mercury drop is charged such that its surface charge density is 2 μC/m2. Exactly 125 such drops are combined to form a big drop. What is the surface charge density of the big drop?

Moderate
Solution

For one drop, if the radius is r and the charge is q, then
σ=q4πr2=2μC/cm2
When 125 drops are combined, the charge on it becomes 125 q and if its radius is R, then
125×43πr3=43πR3R=5r
Charge density of the big drop is
σ1=125q4πR2=125q4π×25r2=5q4πr2=(5×2)μC/cm2

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