Question

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?

 

Answer 1

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 .