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?
-1.5
To find out how many electrons must be transferred from the plate to the rod, let's first convert the charges from microcoulombs to elementary charges.
1 electron charge = 1.6 x 10^-19 C
Given:
Charge of the plate (Qp) = -2.0 µC = -2.0 x 10^-6 C
Charge of the rod (Qr) = +3.0 µC = 3.0 x 10^-6 C
To compare the charges, we need to calculate the difference between Qr and Qp:
Qr - Qp = (3.0 x 10^-6 C) - (-2.0 x 10^-6 C)
= 5.0 x 10^-6 C
Since the charges have opposite signs, the magnitude of the difference is 5.0 x 10^-6 C.
Now, we can determine the number of elementary charges needed to have the same charge:
Number of elementary charges = (Magnitude of difference in charges) / (Charge of one electron)
= (5.0 x 10^-6 C) / (1.6 x 10^-19 C)
Dividing these two values, we find:
Number of elementary charges = 3.125 x 10^13
Therefore, approximately 3.125 x 10^13 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 difference in charge between the two objects and divide it by the elementary charge (e) to find the number of electrons involved.
1. Find the difference in charge between the plate and the rod:
Charge difference = charge on the rod - charge on the plate
Given:
Charge on the plate = -2.0 µC (negative indicates an excess of electrons)
Charge on the rod = +3.0 µC (positive indicates a deficit of electrons)
Charge difference = (+3.0 µC) - (-2.0 µC)
= +5.0 µC
2. Convert the charge difference to coulombs:
1 µC = 1 × 10^-6 C (microcoulomb to coulomb conversion)
Charge difference in coulombs = (+5.0 µC) × (1 × 10^-6 C/µC)
= 5.0 × 10^-6 C
3. Determine the elementary charge (e):
The elementary charge is the charge of a single electron.
e = 1.6 × 10^-19 C
4. Calculate the number of electrons:
Number of electrons = Charge difference / elementary charge
Number of electrons = (5.0 × 10^-6 C) / (1.6 × 10^-19 C)
Using scientific notation, we can rewrite this as:
Number of electrons = 3.125 × 10^13 electrons
Therefore, approximately 3.125 × 10^13 electrons must be transferred from the plate to the rod in order for both objects to have the same charge.