Four identical metallic objects carry the following charges: 1.6, 6.2, −4.8, and −9.4 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 electrons (or protons) make up the final charge on each object?
To solve this problem, we need to apply the conservation of charge principle.
(a) The total charge before the objects touch each other is the sum of the charges on each object:
Total initial charge = 1.6 μc + 6.2 μc - 4.8 μc - 9.4 μc = -5.4 μc
When the objects are brought into contact and separated, the total charge remains the same. Since the four objects are identical, each object would have a final charge of -5.4/4 = -1.35 μc.
(b) To determine the number of electrons (or protons) making up the final charge, we can use the elementary charge value of 1.6 x 10^-19 C.
Number of electrons (or protons) = Final charge / Elementary charge
Number of electrons (or protons) = (-1.35 μc * 10^-6 C/μc) / (1.6 x 10^-19 C)
Number of electrons (or protons) ≈ -8.44 x 10^12
Therefore, the final charge on each object is -1.35 μc, and it is made up of approximately -8.44 x 10^12 electrons (or protons).
To solve this problem, we need to understand that during contact, charges can redistribute themselves to even out. Let's go step-by-step:
Step 1: Calculate the net charge during the contact:
- The sum of the charges is 1.6 + 6.2 - 4.8 - 9.4 = -6.4 μc.
- Since the total charge must be conserved, each object will have a final charge of -6.4/4 = -1.6 μc.
Step 2: Determine how many electrons/protons are required to make up the final charge:
- Since charge is quantized, we know that the elementary charge is 1.6 x 10^(-19) C.
- The final charge on each object is -1.6 μc = -1.6 x 10^(-6) C.
- Dividing the final charge by the elementary charge, we find that each object has -1.6 x 10^(-6) / 1.6 x 10^(-19) ≈ -10^13 electrons/protons.
So, the answers to the given questions are:
(a) The final charge on each object is -1.6 μc.
(b) The final charge on each object is made up of approximately -10^13 electrons/protons.