Question

On a billion $\left( 10^{ 9} \right)$ electrons pass from point P towards another point Q in $\left( 10^{ -3} \right)$ s . What is the current in ampere? What is its direction?

Answer 1

We have given a number of electrons. We can get the total charge on electrons by the product of the number of electrons and the charge on one electron. Now current is given by the ratio of total charge to the time taken. As given electrons are moving from P to Q. Direction of current is always opposite to the direction of electrons.

Complete step-by-step solution:
Given: Number of electrons, $n =10^{ 9}$ .
Time taken, $t =10^{ -3} s$ .
Total Charge is given by the number of electrons multiplied by the charge on one electron.
$Q = ne$
Charge on one electron, $e = 1.6 \times 10^{-19} C$
Therefore, $Q = 10^{9} \times 1.6 \times 10^{-19} C$
$Q = 1.6 \times 10^{-10} C$
Current is defined as the ratio of total charge on an electron to the time taken for traveling the electrons.
$I = \dfrac{Q}{T}$
$\implies I = \dfrac{1.6 \times 10^{-10} C }{10^{-3} s}$
$I = 1.6 \times 10^{-7} A$
Current = $1.6 \times 10^{-7} A$
As electrons are moving from P to Q, then current will move from Q to P.

Note: The most crucial difference between the charge and the current is that the charge is the property of matter, but the current is the rate of charge flow. The charge experiences the force of attraction or repulsion in an electric field. The charge feels the force only in the electrical range, whereas the current feels the force both in the electric and magnetic fields. The electric charges are measured in coulomb, whereas the current is estimated in the amperes.