A plate carries a charge of -3.2 µC, while a rod carries a charge of +1.5 µC. How many electrons must be transferred from the plate to the rod, so that both objects have the same charge?
To find out how many electrons must be transferred from the plate to the rod, we need to determine the charge of a single electron and then calculate the difference in charge between the plate and the rod.
The charge of a single electron is -1.6 x 10^-19 C. This charge is negative because electrons are negatively charged particles.
First, let's convert the charges of the plate and the rod to coulombs:
-3.2 µC = -3.2 x 10^-6 C
+1.5 µC = 1.5 x 10^-6 C
Now, we can calculate the difference in charge between the plate and the rod:
Difference in charge = Absolute value of charge on the plate - Absolute value of charge on the rod
Difference in charge = |-3.2 x 10^-6 C| - |1.5 x 10^-6 C|
Difference in charge = 3.2 x 10^-6 C - 1.5 x 10^-6 C
Difference in charge = 1.7 x 10^-6 C
Since each electron has a charge of -1.6 x 10^-19 C, we can find how many electrons must be transferred by dividing the difference in charge by the charge of a single electron:
Number of electrons = Difference in charge / Charge of a single electron
Number of electrons = (1.7 x 10^-6 C) / (-1.6 x 10^-19 C)
Number of electrons ≈ -1.06 x 10^13 electrons
Therefore, approximately 1.06 x 10^13 electrons must be transferred from the plate to the rod for both objects to have the same charge.