Three identical conducting spheres are placed in a line. From left to right, Qa = 2C, Qb = 3C and Qc = -4C. You touch the spheres all together at the same time and then separate them. What is the charge on sphere A?
Well, I expect they would all be at the same voltage compared to ground.
They are identical so each would have the same charge, the average
(2+3-4)/3 = 1/3 C
To find the charge on sphere A after touching and separating the spheres, we can use the principle of conservation of charge.
The sum of charges before touching must equal the sum of charges after touching.
Given that the charges on the spheres are Qa = 2C, Qb = 3C, and Qc = -4C, the total charge before touching is:
Total charge before touching = Qa + Qb + Qc
= 2C + 3C - 4C
= 1C
When the spheres are touched together, they will redistribute charge among themselves such that the total charge remains the same. In this case, let's assume the charge on sphere A after touching is Qa'.
The total charge after touching and separating is:
Total charge after touching = Qa' + Qb' + Qc'
Since the total charge must be conserved, we can write:
Total charge before touching = Total charge after touching
1C = Qa' + Qb' + Qc'
Given that the spheres are identical, the charge will distribute evenly among the spheres, resulting in Qa' = Qb' = Qc'.
Let's assume the charge on each sphere after touching is Q'
Therefore, we have:
1C = Q' + Q' + Q'
= 3Q'
Solving for Q', we divide both sides of the equation by 3:
Q' = 1C / 3
= 1/3 C
Thus, the charge on sphere A after touching and separating is 1/3 C.
To find the charge on sphere A after touching and separating the spheres, we need to consider the principle of charge conservation. According to this principle, the total charge before and after any interaction remains the same.
Initially, the charges on the spheres are Qa = 2C, Qb = 3C, and Qc = -4C. When you touch them together, the charges redistribute among the spheres, but the total charge remains constant.
Step 1: Calculate the total charge before touching the spheres.
Total charge before = Qa + Qb + Qc = 2C + 3C - 4C = 1C
Step 2: Calculate the total charge after touching and separating the spheres.
Since the total charge remains constant, the total charge after touching and separating the spheres will also be 1C.
Step 3: Distribute the charge among the spheres.
Since the spheres are identical, we can assume that the charges evenly redistribute among them. Therefore, each sphere will have 1C/3 charge.
Step 4: Determine the charge on sphere A.
As each sphere has 1C/3 charge, sphere A will also have 1C/3 charge.
Therefore, the charge on sphere A after touching and separating the spheres is 1C/3.