Question

When a Piece of Polythene is rubbed with wool, a charge of $-2\times {10}^{-7}$ is developed on polythene. The mass transferred to polythene is $\dots \mathrm{kg}$. (A) $11.38\times {10}^{-19}$ (B) $5.69\times {10}^{-19}$ (C) $2.25\times {10}^{-19}$ (D) $9.63\times {10}^{-19}$

Short answer

The mass transferred to polythene is (A) $1.138\times {10}^{-18}\mathrm{kg}$.

Step-by-step solution

Calculate the number of electrons transferred

We know that the charge of a single electron is approximately $e=-1.6\times {10}^{-19}\mathrm{C}$. We're given that the charge developed on polythene is $Q=-2\times {10}^{-7}\mathrm{C}$. To find the number of electrons transferred, we can use the formula: Number of electrons transferred = $\frac{\text{Total Charge}}{\text{Charge of one electron}}$

Calculate the mass transferred

First, find the number of electrons transferred by dividing the total charge (Q) by the charge of one electron (e): Number of electrons transferred = $\frac{-2\times {10}^{-7}}{-1.6\times {10}^{-19}}$ Number of electrons transferred = $1.25\times {10}^{12}$ Now, we need to find the mass of electrons transferred. We know that the mass of a single electron is approximately $m_e=9.1\times {10}^{-31}\mathrm{kg}$. To find the mass transferred, we can multiply the number of electrons transferred by the mass of a single electron: Mass transferred = Number of electrons transferred $\times$ Mass of one electron

Calculate the mass transferred

Calculate the mass transferred by multiplying the number of electrons transferred by the mass of one electron: Mass transferred = $1.25\times {10}^{12}\times 9.1\times {10}^{-31}$ Mass transferred = $1.1375\times {10}^{-18}$ Finally, we can compare our result with the given options: (A) $11.38\times {10}^{-19}\approx 1.138\times {10}^{-18}$ (correct) (B) $5.69\times {10}^{-19}$ (C) $2.25\times {10}^{-19}$ (D) $9.63\times {10}^{-19}$ The correct answer is (A) $1.138\times {10}^{-18}\mathrm{kg}$.

Key concepts

Electrons

Electrons are fundamental particles that are part of an atom. They carry a negative electric charge, denoted by the symbol $e$. The charge of an individual electron is approximately $-1.6\times {10}^{-19}$ coulombs. Electrons are crucial components in electricity and magnetism, forming the backbone for the study of electrostatics.
Electrons reside in the outer regions of atoms, orbiting the central nucleus. They have unique qualities that allow them to move easily between materials, especially during processes such as charging by friction, conduction, and induction. This movement of electrons is known as charge transfer. It plays a vital role in many electrostatic phenomena you'll encounter in physics studies.

Mass of Electron

The mass of an electron is quite small, approximately $9.1\times {10}^{-31}$ kilograms. Despite their tiny mass, electrons significantly balance the electrical environment of an atom. Their mass is a fraction of a proton or neutron's mass, making them much lighter than other subatomic particles within the atom's nucleus.
The mass of electrons becomes critical when considering the transfer of electrons between objects, such as in the rubbed polythene with wool example. When electrons move from one material to another, they carry both charge and mass, albeit very minuscule. Although we often focus on their charge, the mass can be calculated in certain processes, providing insights into small-scale interactions, such as those in electrostatics.

Electrostatics

Electrostatics is the study of electric charges at rest. It explores phenomena related to electric charges that are stationary, unlike in electric currents. Topics under electrostatics include the nature and effects of electric fields, the behavior of charged particles, and the forces they exert on each other.
Key concepts in electrostatics are:

• Electric charge and its properties
• Coulomb's law, which quantifies the force between two charges
• Electric field, which provides a region of influence around a charge
• Electric potential energy and potential difference

Understanding electrostatics helps explain how and why materials become charged and interact with each other through simple actions like rubbing polythene with wool.

Rubbing Polythene with Wool

Rubbing polythene with wool involves a process in electrostatics known as charging by friction. When two different materials, such as polythene and wool, make multiple contacts, electrons can transfer from one material to the other. In this case, electrons move from the wool to the polythene, imparting a negative charge to the polythene.
This process is influenced by:

• The materials' tendency to gain or lose electrons
• The duration and intensity of rubbing
• The surface area of contact between the materials

Such simple actions can lead to fascinating results in electrostatics, creating observable phenomena like static cling or electric shocks. Rubbing certain materials shows practical demonstrations of how seemingly minor interactions can result in significant electrical changes.