Four identical metallic objects carry the following charges: +7.0 µC, +9.0 µC, -4.6 µC, and -1.2 µC. The objects are brought simultaneously into contact, so that each touches the others. Then they are separated
A) What is the final charge on each object?
B) How many protons make up the final charge on each object?
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A) When the objects are brought into contact, the charges redistribute themselves evenly among the objects. Therefore, the total charge remains the same, but it is divided equally among the objects.
Let's first find the total charge:
Total charge = +7.0 µC + 9.0 µC - 4.6 µC - 1.2 µC
Total charge = 10.2 µC - 5.8 µC
Total charge = 4.4 µC
Since there are four objects, the final charge on each object is:
Final charge on each object = Total charge / Number of objects
Final charge on each object = 4.4 µC / 4
Final charge on each object = 1.1 µC
Therefore, the final charge on each object is 1.1 µC.
B) To find the number of protons corresponding to the final charge on each object, we need to convert the charge from microcoulombs to elementary charges (protons).
One elementary charge is equal to 1.6 × 10^-19 coulombs.
Number of protons = Final charge / Elementary charge
Number of protons = 1.1 µC / (1.6 × 10^-19 C)
Now, let's convert the charge to coulombs:
1.1 µC = 1.1 × 10^-6 C
Number of protons = (1.1 × 10^-6 C) / (1.6 × 10^-19 C)
Number of protons ≈ 6.875 × 10^12
Therefore, the number of protons making up the final charge on each object is approximately 6.875 × 10^12.
To determine the final charge on each object, we need to understand how charge distribution works when two objects come into contact and separate again.
When the objects come into contact, charge can be transferred between them. The charges redistribute in a way that aims to equalize the charges between the objects.
To solve this problem, we'll follow these steps:
Step 1: Calculate the total initial charge:
- Total initial charge = Sum of the individual charges
- Total initial charge = +7.0 µC + 9.0 µC - 4.6 µC - 1.2 µC
- Total initial charge = 10.2 µC
Step 2: Divide the total initial charge equally amongst the four objects:
- Final charge on each object = Total initial charge / Number of objects
- Final charge on each object = 10.2 µC / 4
- Final charge on each object = 2.55 µC
So, the final charge on each object after they have come into contact and separated is +2.55 µC.
Now, let's move on to calculating the number of protons that make up this charge on each object.
To calculate the number of protons, we need to know the elementary charge, which is the charge of a single proton.
The elementary charge, denoted as e, is approximately equal to 1.602 x 10^-19 Coulombs.
Step 3: Calculate the number of protons:
- Number of protons = Final charge on each object / Elementary charge
- Number of protons = 2.55 µC / (1.602 x 10^-19 C)
Calculating this gives us the number of protons that make up the final charge on each object.
Please note that due to the large value of the elementary charge and small value of µC, the number of protons may be extremely large in this calculation.
I hope this helps!