Four identical metallic objects carry the following charges: + 1.6, + 6.2, − 4.8, and . 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?
Since they conduct, they will attain the same electric potential after they touch. Since they are alike, they will each have the same charge to produce that potential. Figure out what that charge is. Divide than by "e", the electron charge, for the number of electrons or protons. Since it will be postive, there will be extra protons.
To determine the final charge on each object, we need to apply the principle of charge conservation. According to this principle, the total charge before and after the objects come into contact remains the same.
Step 1: Calculate the initial total charge before the objects come into contact.
The initial total charge is the sum of the individual charges:
+1.6 + (+6.2) + (-4.8) + (unknown charge) = initial total charge.
Step 2: Determine the unknown charge after contact.
Since all the objects are identical and contact each other simultaneously, their charges are evenly distributed among them. This means that the initial total charge is divided equally among the four objects. In other words, each object now has a charge that is one-fourth of the initial total charge.
Let's call the unknown charge on each object "Q."
Q + Q + Q + Q = initial total charge / 4.
Simplifying the equation, we have:
4Q = initial total charge / 4.
Step 3: Calculate the unknown charge.
To find the unknown charge, divide the initial total charge by 4:
Q = (initial total charge) / 16.
This value of Q represents the final charge on each object.
(a) The final charge on each object is (initial total charge) / 16.
(b) To determine the number of electrons or protons that make up the final charge on each object, we can use the elementary charge (e). The elementary charge represents the charge carried by a single electron or proton and is approximately 1.6 x 10^-19 coulombs.
To find the number of elementary charges in the final charge (Q), divide Q by the elementary charge:
Number of elementary charges = Q / (elementary charge).
This will give you the approximate number of electrons (if the charge is negative) or protons (if the charge is positive) that make up the final charge on each object.