A Metal sphere A has a charge of +6 units and an identicalmetal sphere, B, has a charge of -4 units. If the spheres are brought into contact with each other and then seperated, the charge on sphere B will be _______. College Physics, equation or work would be nice. Thanks ^^^^
One way to think about it is (not really but way to figure)
there are 6 extra protons on A
There are 4 extra electrons on B
If you bring them together you will be left with 2 protons to split between them
They will each have a charge of +1
To determine the charge on sphere B after contact and separation, we can use the principle of conservation of charge. According to this principle, the total charge before and after the interaction should remain the same.
Initially, Sphere A has a charge of +6 units, and Sphere B has a charge of -4 units.
When the spheres are brought into contact, charge can flow between them until they reach equilibrium. Since the charges are equal in magnitude, +6 and -4, the total charge is +6 - 4 = +2 units.
After contact, the charges distribute themselves evenly across both spheres, and the resulting charge on each sphere will be the average of their initial charges. Since there are two equal spheres, the average charge on each sphere will be +2/2 = +1 unit.
Therefore, after separation, the charge on Sphere B will be +1 unit.
This can be summarized using the equation:
(Q_initial A + Q_initial B) / 2 = (Q_final A + Q_final B) / 2
Where:
- Q_initial A = initial charge on Sphere A
- Q_initial B = initial charge on Sphere B
- Q_final A = final charge on Sphere A
- Q_final B = final charge on Sphere B
In this case, Q_initial A = +6 units and Q_initial B = -4 units. Q_final A is also +1 unit, and we want to find Q_final B.
Simplifying the equation, we get:
(6 - 4) / 2 = (1 + Q_final B) / 2
2 / 2 = (1 + Q_final B) / 2
1 = 1 + Q_final B
Q_final B = 0
Therefore, the charge on Sphere B after separation will be 0 units.
To determine the charge on sphere B after being brought into contact with sphere A and then separated, we need to apply the principle of charge conservation.
According to the principle of charge conservation, the total charge before and after the spheres are brought into contact remains constant. In other words, the total charge on the two spheres combined remains the same.
Initially, sphere A has a charge of +6 units, and sphere B has a charge of -4 units. Therefore, the total charge before bringing the spheres into contact is:
Total charge = Charge of sphere A + Charge of sphere B
Total charge = +6 units + (-4 units)
Total charge = +2 units
When the spheres are brought into contact, they will redistribute their charges in order to reach a new equilibrium. Since the spheres are identical, an equal amount of charge will be transferred between them.
In this case, since sphere A has a higher positive charge (+6) and sphere B has a lower negative charge (-4), electrons will flow from sphere A to sphere B to equalize their charges. The charge transferred will be equal to the difference in their original charges.
Charge transferred = |Charge of sphere A - Charge of sphere B|
Charge transferred = |6 units - (-4 units)|
Charge transferred = |6 units + 4 units|
Charge transferred = |10 units|
Charge transferred = 10 units
After the spheres are separated, sphere A will have lost 10 units of positive charge, and sphere B will have gained 10 units of negative charge. Therefore, the final charge on sphere B will be:
Charge on sphere B = Initial charge of sphere B + Charge transferred
Charge on sphere B = -4 units + 10 units
Charge on sphere B = +6 units
Hence, the charge on sphere B will be +6 units after being brought into contact with sphere A and then separated.
The equation used was the principle of charge conservation, which states that the total charge of an isolated system remains constant. The work involved was the calculation of the charge transferred between the spheres, which is equal to the difference in their initial charges.