Question

A T.V set shoots out a beam of electrons. The beam current is \[10\,A\]. How many electrons strike the T.V screen in a minute?

Answer 1

Hint:Current is the amount of charge passing through a conductor per unit time. The S.I unit of electric current is Ampere. It’s a simple numerical which can be done using two formulae which are \[q=it\] and \[q=ne\]

Complete step by step answer:
First of all, let’s find the amount of charge in this beam of electrons which can be found out by using the formula:
\[q=it\]
Where \[q\] is a charge and its S.I unit is Coulomb, \[i\]is the amount of current in amperes, \[t\]is the time in seconds.
Therefore, substituting all the values from question, we get,
\[q=10A\times 60\operatorname{s}=600C\]

As charge is always quantized in nature, the net charge of the body can be expressed as the integral multiples of the basic unit of charge. Mathematically, it can be written as:
\[q=ne\]
Where\[n\] is the number of electrons. It represents an integer and cannot be a fraction. \[e\] is the charge on one electron which is equal to \[1.6\times {{10}^{-19}}C\].
Therefore,
\[n=\dfrac{q}{e}\\
\Rightarrow n=\dfrac{600}{1.6\times {{10}^{-19}}}\\
\therefore n=375\times {{10}^{19}}\text{ electrons}\]

Hence, $375\times {{10}^{19}}$ electrons strike the T.V screen in a minute.

Note: The units in this question could have been changed and then you would have to convert those units into their S.I units respectively. So it is wise to remember the conversions. The other common units of charge are micro-coulomb or milli-coulomb. Microcoulomb is denoted as \['\mu C'\] and milli-coulomb is denoted as \['mC'\]. The Conversion factor from microcoulomb to coulomb is:
\[1\mu C={{10}^{-6}}\,C\]
Similarly, the conversion factor from milli coulomb to coulomb is:
\[1mC={{10}^{-3}}\,C\]