In: Physics

Two identical metal spheres A and B are connected by a plastic rod. Both are initially neutral. 4.0×1012 electrons are added to sphere A, then the connecting rod is removed. a)Afterward, what is the charge of A? b)Afterward, what is the charge of B?

Concepts and reason

The required concepts to solve the problem are electric charges and conduction of electric charges. First, find the charge on sphere A from the relation between the number of electrons and the electron's charge. Then, find the charge on sphere B using the relation between the number of electrons and the electron's charge.

Fundamentals

Electric charge is a property of the object to interact with the electromagnetic field. Charges can be of two types, positive and negative. Conduction is a process through which charge is transferred from one charged particle to another. Through conduction, the neutral object acquires the same charge as the charged object. The charge on a positive plate is, \(q=n e\)

Here, \(n_{\text {is the number of electrons added and }} e_{\text {is the electronic charge. }}\) The charge on a negative plate is, \(q=n(-e)\)

(a) The charge on sphere \(\mathrm{A}\) is,

$$ q_{A}=n(-e) $$

Substitute \(4.0 \times 10^{12}\) for \(n\) and \(1.6 \times 10^{-19} \mathrm{C}\) for \(e .\)

$$ \begin{aligned} q_{A} &=\left(4.0 \times 10^{12}\right)\left(-1.6 \times 10^{-19} \mathrm{C}\right) \\ &=-6.4 \times 10^{-7} \mathrm{C} \\ &=-640 \mathrm{nC} \end{aligned} $$

Part a

The charge on sphere \(A\) is \(-640 \mathrm{nC}\).

As the electrons are added to the neutral sphere, the charge acquired by sphere A becomes negatively charged. The total charge of the sphere depends on the total number of electrons and the electronic charge.

(b) The charge acquired by sphere \(\mathrm{B}\) is zero. The spheres are connected by a plastic rod, which is not a conductor. So, no charge is transferred through the plastic rod.

Part b

The charge on sphere \(\mathrm{B}\) is 0 .

The charge is transferred through a conductor. The two metallic spheres are connected with a plastic rod, which is an insulator. So, no charge is transferred through the rod. As initially, the rods were neutral, the charge on sphere \(\mathrm{B}\) is zero.

Part a

The charge on sphere \(A\) is \(-640 \mathrm{nC}\).

Part b

The charge on sphere \(\mathrm{B}\) is 0 .

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