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Question

64 droplets of mercury each of radius r and carrying charge q, coalesce to form a big drop. Compare the surface density of charge of each drop with is that of the big drop.

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Solution

Given that,

Droplets of mercury = 64

Density of small droplet =σsmall

Density of big droplet =σbig

We know that,

σsmallσbig=qQ×R2r2

σsmallσbig=q(nq)×n13rr2

σsmallσbig=n13

Now, put the value of n

σsmallσbig=(64)13

σsmallσbig=14

Hence, the ratio is 14


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