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Question: A polythene piece rubbed with wool is found to have a negative charge of \(3 \times 10^{-7}\)C. a....

A polythene piece rubbed with wool is found to have a negative charge of 3×10−73 \times 10^{-7}C.
a. Estimate the number of electrons transferred ( from which to which )?
b. Is there any transfer of mass from wool to polythene?

Explanation

Solution

If there is an excess of electrons, the charge on the body will be negative whereas if there is a deficiency of electrons, the charge on the body will be positive. As electrons are also a part of matter, they also have well-defined mass. Hence, whenever there’s a transfer of charge, mass also gets exchanged. But the change in mass is negligible so one can proceed without considering it.

Formula used:
q=neq = ne where q is the charge transferred when ‘n’ number of electrons carrying charge ‘e’ on each is exchanged.

Complete step by step answer:
Given the charge is transferred such that the polythene piece gets a negative charge of 3×10−73 \times 10^{-7}C. This means polythene has an excess of electrons. Hence electrons must be transferred from wool to polythene.
For number of electrons, putting the value of charge in the equation q=neq = ne, we get;
3×10−73 \times 10^{-7}= n (1.6×10−191.6 \times 10^{-19})
n=3×10−71.6×10−19n = \dfrac{3 \times 10^{-7}}{1.6 \times 10^{-19}}=1.875×10121.875 \times 10^{12}
Hence a total of 1.875×10121.875 \times 10^{12}electrons are transferred from wool to polythene.
Mass: To find the mass transferred from wool to polythene, mass of one electron (mem_e) = 9.1×10−31kg9.1 \times 10^{-31} kg
Hence total mass of n electrons = n×men \times m_e=1.875×10121.875 \times 10^{12} ×\times 9.1×10−319.1 \times 10^{-31}= 1.706×10−181.706 \times 10^{-18}kg.
So a total of 1.706×10−181.706 \times 10^{-18}kg of mass is transferred from wool to polythene.

Note:
We can see that mass is very negligible, hence it could be neglected. It’s important to realize that if a negative charge is in excess, it means some electrons must be transferred from some other body. But if we say that positive charge in excess, it doesn’t imply that protons are transferred. In fact, protons don’t move at all! They are just present inside the nucleus. Rather positive charge means a deficiency of electrons.