Question

An electron moves in a circle of radius of 1.0cm with a constant speed of 4.0106m/s, electric current at a point on the circle will be: $\left( {e = - 1.6 \times {{10}^{ - 19}}C} \right)$
A $1 \times {10^{ - 11}}\Omega $
B $1.1 \times {10^{ - 7}}\Omega $
C $5.1 \times {10^{ - 7}}\Omega $
D $2.1 \times {10^{ - 7}}\Omega $

Answer 1

Hint: Electric current is defined as the rate of flow of charge at a certain point or region. The existence of electric current depends on the flow of electric charges. Electric current generally carried by the charged particles .The direction of electric current depends on the direction of flow of positive charges. The SI unit of charge is Coulomb; it is represented by $C$. The SI unit of electric Current is $Coulomb/\operatorname{Sec} ond $ or $ Ampere$.Current generally flows opposite to the direction of flow of electrons.

Complete Solution step by step:
Radius of circle $R = 1.0cm$.
Speed of electron along the circular path$ = 4.0 \times {10^6}m/s.$
Constant value of electron or charge $e = - 1.6 \times {10^{ - 19}}C$
As we know the length of wire which forms circular path will be: $2\pi R$
Length of wire$L = 2\pi \times 1$
    $ = 2 \times 3.14 \times 1$
    $ = 6.28cm$
    $ = 0.063m$
Since $\left( {1cm = 0.01m} \right)$
For time, \[Time = \dfrac{{Length\,of\,wire\,L}}{{Speed\,of\,electron}}\]
$Time = \dfrac{{0.628}}{{4.0 \times {{10}^6}}}$
$ = 0.015 \times {10^{ - 6}}\sec $
As we know, \[Current\,i = \dfrac{{Charge\,\,Q}}{{Time\,t}}\]
Current $\,i = \dfrac{{1.6 \times {{10}^{ - 19}}}}{{0.015 \times {{10}^{ - 6}}}}$
$ = 1.1 \times {10^{ - 11}}\Omega $
Hence, the correct option is A.


Note: Be sure to know that the electric current generally flows from higher potential difference to lower potential difference. Electric current flows slightly lesser than that of the light; generally, it can flow in conductors only. The total charge transferred by the electric current will be equal to the product of current in amperes and that of time in seconds.