Four identical metallic spheres with charges of +2.2 µC, +8.2 µC, −4.6 µC, and −9.2 µC are placed on a piece of paper. The paper is lifted on all corners so that the spheres come into contact with each other simultaneously. The paper is then flattened so that the metallic spheres become separated.
(a) What is the resulting charge on each sphere?
(b) How many excess or absent electrons (depending on the sign of your answer to part (a) correspond to the resulting charge on each sphere?
resulting charge. Add the charges, divide by four.
b. divide the charge on each sphere by the charge of one electron.
To determine the resulting charge on each sphere after coming into contact with each other, we need to apply the principle of charge conservation. According to this principle, the total charge before and after the interaction remains the same.
(a) Since the spheres come into contact simultaneously, they will redistribute their charges until they reach equilibrium. Let's denote the charge on the spheres after this redistribution as q1, q2, q3, and q4, respectively.
The total initial charge is the sum of the individual charges: Qinitial = +2.2 µC + 8.2 µC - 4.6 µC - 9.2 µC = -3.4 µC.
According to charge conservation, the total charge after redistribution must be equal to the initial charge: Qfinal = Qinitial = -3.4 µC.
Since all the spheres are identical, they will split the total charge equally. Therefore, the resulting charge on each sphere is: q1 = q2 = q3 = q4 = -3.4 µC / 4 = -0.85 µC.
(b) To determine the number of excess or absent electrons corresponding to the resulting charge on each sphere, we need to convert the charge into the number of elementary charges. One elementary charge has a magnitude of 1.6 x 10^-19 C.
The number of excess or absent electrons can be calculated using the formula: n = q / e, where n is the number of electrons, q is the charge, and e is the elementary charge.
For each sphere, the resulting charge is -0.85 µC. So, the number of excess or absent electrons for each sphere can be calculated as follows:
n = -0.85 µC / (1.6 x 10^-19 C) ≈ -5.3 x 10^18 electrons.
Note: Since the charge is negative, it means there is an excess of electrons compared to a neutral sphere. The negative sign indicates the excess of negative charges (electrons).
Therefore, the resulting charge on each sphere is approximately -0.85 µC, which corresponds to an excess of approximately 5.3 x 10^18 electrons.
To determine the resulting charge on each sphere, you need to apply the Principle of Conservation of Charge. According to this principle, the total charge in a system remains constant unless an external charge is introduced.
Step 1: Calculate the total initial charge
Add up the charges of the spheres: (+2.2 µC) + (+8.2 µC) + (-4.6 µC) + (-9.2 µC) = -3.4 µC
Step 2: Divide the total charge equally among the spheres
Since all the spheres are identical, the total charge should be divided equally among them. Divide the total charge (-3.4 µC) by the number of spheres (4) to get the individual charge on each sphere.
-3.4 µC / 4 = -0.85 µC
(a) So, the resulting charge on each sphere is -0.85 µC.
Step 3: Calculate the excess/deficit of electrons
To determine the excess or deficit of electrons, you need to know the charge of a single electron. The elementary charge is approximately -1.6 x 10^-19 C.
Divide the charge of each sphere (-0.85 µC) by the charge of a single electron (-1.6 x 10^-19 C) to find the number of excess or absent electrons.
-0.85 µC / (-1.6 x 10^-19 C) ≈ 5.31 x 10^18 electrons
(b) So, the resulting charge on each sphere corresponds to approximately 5.31 x 10^18 excess or absent electrons.