Final answer:
The charged objects A and B have different masses due to the transfer of electrons during induction. Object A, which gained electrons and hence mass, ends up weighing more than object B, which lost electrons.
Step-by-step explanation:
The process of charging by induction involving metal spheres can change their charge without direct contact by using a charged object. When a charged object is brought near one of the neutral spheres, it causes electrons to redistribute between the spheres, leaving one with a negative charge and the other with a positive charge after they are separated. The concept of conservation of charge dictates that the total charge before and after separation remains constant. It is important to note that while the charge is transferred, mass can also be transferred in the form of electrons. Since electrons have a very small mass, this mass change is typically negligible, but it can be calculated.
When object A is charged by induction and acquires a charge of -3.0*10⁻⁶ C, it gains that amount of electrons. Conversely, when object B is charged by induction to a charge of +3.0*10⁻⁶ C, it loses the same amount of electrons. Knowing that the mass of an electron is approximately 9.109× 10⁻³± kg, we can calculate the difference in mass. The mass of electrons gained by object A is equal to the number of electrons times the mass of an electron. Since object B loses electrons, it will be lighter than object A by that same amount.
Considering the charge of an electron is 1.602× 10⁻ C, we can find the number of electrons transferred by:
- Number of electrons = Total charge / Charge of one electron
- Number of electrons = 3.0× 10⁻⁶ C / 1.602× 10⁻ C/e⁻
- Number of electrons ≈ 1.875× 10⁻⁷
The difference in mass between the charged objects is:
- Mass difference = Number of electrons × Mass of one electron
- Mass difference = 1.875× 10⁻⁷ e⁻ × 9.109× 10⁻³± kg/e⁻
- Mass difference ≈ 1.707× 10⁻ kg
Thus, object A, which gained electrons, has the greater mass compared to object B, which lost electrons.