Problem 26 - Master Resource Book in JEE Main Physics

Question

A polythene piece, rubbed with wool, is found to have negative charge of \(4 \times 10^{-7}\) C. The number of electrons transferred from wool to polythene is (a) \(1.5 \times 10^{12}\) (b) \(2.5 \times 10^{12}\) (c) \(2.5 \times 10^{13}\) (d) \(3.5 \times 10^{13}\)

Step-by-Step Solution

Answer

The number of electrons transferred is \(2.5 \times 10^{12}\).

Step 1: Understand the Charge of an Electron

Every electron carries a negative charge of approximately \(-1.6 \times 10^{-19}\) coulombs. This information is crucial for finding out how many electrons correspond to the given charge on the polythene.

Step 2: Calculate the Number of Electrons

To find out how many electrons were transferred, use the formula for the number of electrons \( n = \frac{q}{e} \), where \( q = 4 \times 10^{-7} \) C is the total charge and \( e = 1.6 \times 10^{-19} \) C is the charge of an individual electron.

Step 3: Perform the Calculation

Substitute the known values into the formula:\[ n = \frac{4 \times 10^{-7}}{1.6 \times 10^{-19}}\]Calculate \( n \) by dividing the total charge by the charge of one electron:\[ n = \frac{4}{1.6} \times 10^{12} = 2.5 \times 10^{12}\]This indicates that \(2.5 \times 10^{12}\) electrons were transferred from the wool to the polythene.

Key Concepts

Charge of an Electron

Every electron carries a fundamental property known as electric charge. This charge is negative and is approximately \(-1.6 \times 10^{-19}\) coulombs. Understanding this is essential when dealing with electrostatics. Electrons are the primary carriers of electrical charge in materials.

• A single electron has a very small charge but, collectively, they can amount to significant levels of charge.
• This charge is fixed and universal, making calculations consistent and reliable.

The magnitude of the charge of an electron is very small, which is why we observe large numbers when counting transferred electrons, as in this exercise. Knowing the charge of a single electron allows us to determine how many electrons make up a given amount of total charge.

Electron Transfer

When objects come into contact and rub against each other, electrons can transfer from one to the other. This process is often behind the build-up of static electricity. In this exercise, a polythene piece rubbed with wool achieved a negative charge because electrons transferred from wool to it.

• Electron transfer is fundamentally about the movement of these charged particles between substances.
• Objects that gain electrons become negatively charged, while those that lose electrons become positively charged.

The number of transferred electrons can be calculated if we know the total charge an object has acquired. This understanding is applied using the formula \(n = \frac{q}{e}\), where \(q\) is the total charge and \(e\) is the charge of one electron.

Coulombs

Coulombs are the standard unit of electric charge in the International System of Units (SI). They are named after Charles-Augustin de Coulomb, a French physicist.

• Charge is frequently measured in coulombs because they create a consistent and standard method of quantifying electric charge.
• For practical purposes, other units or multiples like microcoulombs or picocoulombs can be used, especially when dealing with small charges typical in electrostatics.

In electrostatic calculations, understanding the use of coulombs is crucial to carrying out correct conversions and computations, such as determining how many electrons were transferred in a process, as shown in the exercise.