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?
To answer this question, we need to understand how charges are distributed when metallic spheres come into contact and how they redistribute when the spheres separate.
When metallic spheres come into contact, they share their charges through a process called charging by conduction. In this process, electrons can move freely between the spheres until they reach equilibrium. The total charge remains the same, but it gets redistributed among the spheres.
(a) To find the resulting charge on each sphere, we need to calculate the total charge and divide it equally among the spheres. Let's go step by step:
Step 1: Calculate the total charge
Total charge = +2.2 µC + 8.2 µC - 4.6 µC - 9.2 µC
Total charge = -3.4 µC
Step 2: Divide the total charge equally among the spheres.
Since there are four identical spheres, we divide the total charge by 4.
Resulting charge on each sphere = (-3.4 µC) / 4
Resulting charge on each sphere = -0.85 µC
Therefore, the resulting charge on each sphere is -0.85 µC.
(b) To determine the number of excess or absent electrons corresponding to the resulting charge on each sphere, we can use the elementary charge (e) and the definition that 1 μC (microcoulomb) is equivalent to 1 x 10^(-6) C (coulomb).
Step 1: Convert the resulting charge on each sphere to coulombs.
Resulting charge = -0.85 µC = -0.85 x 10^(-6) C
Step 2: Calculate the number of elementary charges using Q = Ne, where:
Q = resulting charge in coulombs
N = number of excess or absent electrons
e = elementary charge = 1.6 x 10^(-19) C
N = Q / e
N = (-0.85 x 10^(-6) C) / (1.6 x 10^(-19) C)
N ≈ -5.3 x 10^12
Therefore, the resulting charge on each sphere corresponds to approximately -5.3 x 10^12 absent electrons.