Question

Two identical metal spheres a and b are in contact. both are initially neutral. 1.0×1012 electrons are added to sphere a, then the two spheres are separated. you may want to review ( pages 639 - 641) . part a afterward, what is the charge of sphere a?

Answer 1

Metal is conductive, so electrons will transfer onto sphere b until there is an equal number of electrons on either sphere (the electrical gradient will be zero). This means that 5 x 10^11 electrons will be on either sphere, and since the charge of an electron is 1.602 x 10^-19 Coulombs, multiplying this by the number of electrons gives a charge of 8.01 x 10^-8 Coulombs, or 80.1 nanocoulombs.

Answer 2

The charge on the sphere A and sphere B after they are separated is $\boxed{ - 80\,{\text{nC}}}$ each.

Further Explanation:

Given:

The number of electrons transferred to sphere $A$ is  $1.0 \times {10^{12}}$.

Concept:

The amount of charge carried by the electrons when reaches the spheres kept in contact with each other is first distributed equally on each sphere. Later as the spheres are moved away from one another, the charge on each sphere remains the same as it was when they were in contact.

The amount of charge on one electron is $- 1.6 \times {10^{ - 19}}\,{\text{C}}$.

So, the amount of charge carried by the $1.0 \times {10^{12}}$ electrons is given as.

$\begin{aligned}Q&= \left( {1.0 \times {{10}^{12}}} \right)\left( { - 1.6 \times {{10}^{ - 19}}} \right)\\&= - 1.6 \times {10^{ - 7}}\,{\text{C}}\\\end{aligned}$  

Since the charge is disturbed equally on the two sphere, so the amount of charge carried by each sphere s half of the total charge.

$\begin{aligned}{Q_A}&= \frac{{ - 1.6 \times {{10}^{ - 7}}}}{2}\\&= - 8 \times {10^{ - 8}}\,{\text{C}}\\ &= - 8{\text{0}}\,{\text{nC}}\\\end{aligned}$  

Thus, the amount of the charge carried by each sphere after separating from each other is $\boxed{ - 80\,{\text{nC}}}$.

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Answer Details:

Grade: College

Chapter: Electrostatics

Subject: Physics

Keywords: Metal spheres, two identical, in contact, neutral, charged, electrons, charge on electron, charge on metallic sphere, charge of sphere A.