A polythene piece rubbed with wool is found to have a negative charge of \(3×10^{–7} C\)

Question Id: PH0000011

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

(a) Estimate the number of electrons transferred (from which to which?) 

(b) Is there a transfer of mass from wool to polythene?

Answer: 

(a) From wool to polythene 

(b) Yes, but amount of mass is very less \(1.7079 \times 10^{-18} Kg\)

Explanation: 

(a) As we know an atom has neutral charge because it has same number of  electron and proton. Charge of an atom or object depends on number of electron loss or gain. If any atom gain electron then it gets negatively charge (due to negative charge of electron) or if any atom loss electron then it gets positive charge (because number of electron is less than number f proton). 

 

As polythene is fund to be negative charge that means electron is transferred from wool to polythene.

From the quantisation of charge one can say that any amount of  discrete charge (Q) is integral multiple of electronic charge(e) i.e \(Q=ne\)  ; where n is positive integer number (n=0,1,2,3.....) 

Given, \(Q= 3 \times 10^{-7}\) and \(e=1.6 \times 10^{-19} C\)

Now we know that

\[Q=ne\]

\[\implies n=\frac{Q}{e}\]

\[\implies n=\frac{3 \times 10^{-7}}{1.6 \times 10^{-19}}\]

\[\implies n=1.875 \times 10^{12}\]

Hence, \(1.875 \times 10^{12}\) number of electron has been transferred froom wool to polythene.

Fig-1: Quantisation of charge

(b) An electron has mass \(m=9.109 \times 10^{-31}Kg\).

As \(1.875 \times 10^{12}\) number of electron has transferred from wool to polythene so amount f mass(M) transfererd from wool to polythene is 

\[M=n \times m\]

\[M= 1.875 \times 10^{12} \times 9.109 \times 10^{-31}\]

\[M=17.079 \times 10^{-19}\]

\[M=1.7079 \times 10^{-18}\]

So, there must be some transferred of mass from wool to polythene but the amount of mass is very very less i.e \(1.7079 \times 10^{-18} Kg\).