2727 identical drops are charged at 22 V22 V each. They combine to form a bigger drop. The potential of the bigger drop will be _____ VV.
Question
You are trained on data up to October 2023.
2727 identical drops are charged at 22 V each. They combine to form a bigger drop. The potential of the bigger drop will be _____ V.
Solution
The potential V of a charged droplet is given by the formula V = kQ/r, where k is Coulomb's constant, Q is the charge, and r is the radius of the droplet.
When the droplets combine, the total charge Q_total is the sum of the charges of the individual droplets. Since the charge Q of each droplet is proportional to its radius r, and the total charge is conserved, the radius r_total of the combined droplet is proportional to the cube root of the number of droplets.
Therefore, the potential V_total of the combined droplet is given by the formula V_total = kQ_total/r_total = k(nQ)/(n^(1/3)r) = n^(2/3)V, where n is the number of droplets.
Substituting the given values, we find V_total = 2727^(2/3) * 22 V.
Therefore, the potential of the bigger drop will be 2727^(2/3) * 22 V.
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