A plate carries a charge of -2.0 µC, while a rod carries a charge of +3.0 µC. How many electrons must be transferred from the plate to the rod, so that both objects have the same charge?
To determine the number of electrons that must be transferred from the plate to the rod, we need to compare the charges of the two objects and calculate the difference between them.
1. Convert the charges to the elementary charge unit:
-2.0 µC = -2.0 × 10^(-6) C
+3.0 µC = +3.0 × 10^(-6) C
2. Determine the difference in charge between the plate and the rod:
Charge difference = Absolute value of charge of plate - Absolute value of charge of rod
Using the above values, the charge difference is:
Charge difference = |-2.0 × 10^(-6) C - 3.0 × 10^(-6) C|
3. Calculate the elementary charge (charge of a single electron):
Elementary charge = 1.6 × 10^(-19) C
4. Divide the charge difference by the elementary charge to find the number of electrons transferred:
Number of electrons transferred = (Charge difference) / (Elementary charge)
Substituting the values into the equation, we get:
Number of electrons transferred = |-2.0 × 10^(-6) C - 3.0 × 10^(-6) C| / (1.6 × 10^(-19) C)
Simplifying this expression, we have:
Number of electrons transferred = (5.0 × 10^(-6) C) / (1.6 × 10^(-19) C)
5. Evaluate the expression using a calculator:
Number of electrons transferred ≈ 3.125 × 10^13
Therefore, approximately 3.125 × 10^13 electrons must be transferred from the plate to the rod so that both objects have the same charge.