Eight identical spherical raindrops are each at a potential V relative...
**Coalescence of Identical Raindrops**
When identical spherical raindrops are close to each other, they experience mutual attractive forces due to the difference in their electric potentials. These forces cause the raindrops to move towards each other and eventually coalesce into one larger raindrop. The potential of the resulting raindrop can be determined by considering the conservation of charge.
**Conservation of Charge**
The total charge of the system remains constant throughout the coalescence process. Since the raindrops are identical, each raindrop has the same charge, q. Therefore, the total charge of the system before and after coalescence is given by:
Q_initial = 8q
Q_final = q
**Potential Difference and Charge**
The potential difference, V, between a raindrop and the potential far away is directly proportional to the charge of the raindrop. Therefore, the initial potential of each raindrop is given by:
V_initial = kq
where k is a constant.
**Potential of the Resulting Raindrop**
When the raindrops coalesce, their charges combine to form the charge of the resulting raindrop. Since the total charge is conserved, we can equate the initial and final charges:
Q_initial = Q_final
8q = q
Simplifying the equation, we find that q = 1/8.
Therefore, the potential of the resulting raindrop, V_final, is given by:
V_final = kq
V_final = k(1/8)
V_final = (1/8)V
**Value of n**
The value of n represents the ratio of the potential of the resulting raindrop to the potential of each initial raindrop. From the previous calculations, we determined that the potential of the resulting raindrop is (1/8)V. Therefore, the value of n is 1/8.
Hence, the potential of the resulting raindrop is 1/8 times the potential of each initial raindrop.
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