If 109 electrons move out of a body to another body every second, how much time is required to get a total charge of 1 C on the other body?
Question
If 109 electrons move out of a body to another body every second, how much time is required to get a total charge of 1 C on the other body?
Solution
Step 1: Understand the problem We know that 109 electrons are moving from one body to another every second. We also know that each electron carries a charge of 1.6 × 10^-19 C (coulombs). We want to find out how long it will take for the second body to accumulate a total charge of 1 C.
Step 2: Calculate the charge transferred per second First, we need to calculate how much charge is being transferred every second. We do this by multiplying the number of electrons by the charge of each electron. So, 109 electrons x 1.6 × 10^-19 C/electron = 1.6 × 10^-10 C. This is the amount of charge transferred every second.
Step 3: Calculate the time required for 1 C to accumulate Next, we need to calculate how long it will take for the second body to accumulate a total charge of 1 C. We do this by dividing the total charge we want (1 C) by the charge transferred per second (1.6 × 10^-10 C/s). So, 1 C ÷ 1.6 × 10^-10 C/s = 6.25 × 10^9 seconds.
Step 4: Convert seconds to years To make this time more understandable, we can convert it to years. There are 365 days in a year, 24 hours in a day, and 3600 seconds in an hour. So, 6.25 × 10^9 seconds ÷ (365 days/year x 24 hours/day x 3600 seconds/hour) = approximately 198 years.
So, it would take approximately 198 years for the second body to accumulate a total charge of 1 C, if 109 electrons are moving from the first body to the second body every second.
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