Question

A beam of electrons emitted from the electron gun G is accelerated by an electric field E. The area of cross section of the beam remains constant. As the beam moves away from G

• A. the speed of the electrons increases
• B. the current constituted by the beam increases
• C. the number of electrons per unit volume in the beam increases
• D. the number of electrons per unit volume in the beam decreases

Answer 1

Answer: (A), (D)

The correct options are
A the speed of the electrons increases
D the number of electrons per unit volume in the beam decreases

Since, beam of electrons emitted from the electron gun G is accelerated by an electric field E, the speed of the electrons increases (due to acceleration). The current I remains constant, as the number of electrons emitted per second by the gun is constant.
Now ,
$I=neA{v}_d$
$v_d=\frac{I}{eAn}$
Where, n is number of electrons per unit volume in the beam, e is charge on electrons, A is area of cross section of beam of electrons and $v_d$ is drift velocity of electrons.
As I, A and e are constant,
$v_d\propto \frac{1}{n}$
Hence, when $v_d$ increase, n must decrease.