Question

When a piece of polythene is rubbed with wool, a charge of \[ - 2 \times {10^{ - 7}}C\] is developed on polythene. What mass is transferred to polythene?
A \[5.69 \times {10^{ - 19}}kg\]
B \[2.25 \times {10^{ - 19}}kg\]
C \[9.63 \times {10^{ - 19}}kg\]
D \[11.38 \times {10^{ - 19}}kg\]

Answer 1

Hint: When a piece of polythene is rubbed with wool, some amount of electrons get transferred from wool to polythene. That’s why wool becomes positively charged and polythene becomes negatively charged. Therefore some mass is transferred to polyethylene because an electron has mass.

Formula used:
To calculate the net mass that transfers to polythene we can use,
\[M = \dfrac{{{m_e}}}{e} \times q\]

Complete step by step solution:
Let, the amount of charge transferred to polythene is \[q = - 2 \times {10^{ - 7}}C\] and charge of one electron \[e = - 1.6 \times {10^{ - 19}}C\]
The number of electrons transfer to polythene from wool is \[n\]
As we know \[q = ne\], therefore,
\[n = \dfrac{q}{e}\]\[ = \dfrac{{ - 2 \times {{10}^{ - 7}}}}{{ - 1.6 \times {{10}^{ - 19}}}}C\]\[ = 1.25 \times {10^{12}}C\]
Mass of an electron \[{m_e} = 9.1 \times {10^{ - 31}}kg\]
Total mass transfer from wool to polythene \[M = \dfrac{{{m_e}}}{e} \times q\]
Or, \[M = {m_e} \times n\]
\[M = 9.1 \times {10^{ - 31}} \times 1.25 \times {10^{12}}kg\]\[ = 11.38 \times {10^{ - 19}}kg\]
\[\therefore \]The correct answer is option D.

Note:
Transfer of electron is when a negatively charged object tries to get rid of the excess electron by transferring it to another object.
There are three different ways to transfer electrons.
Charging by friction- Transfer of electrons by friction occurs when an object is rubbed against another object, energy is provided from outside by friction. This energy is used to remove electrons from one object to another.
Charging by conduction- When a neutral object is brought to a charged object, electrons are transferred to the neutral object from the charged object. Then, the neutral object becomes charged. Conducting charing involves the physical connection of two bodies.
Charging by induction- By induction, a body can be charged when the body is brought to the electric field. Induction charging doesn't need any physical connection.