Question

In hydrogen discharge tube, it is observed that through a given cross-section $3.13 \times {10^{15}}$ electrons are moving from right to left and $3.12 \times {10^{15}}$ protons are moving from left to right. The current in the discharge tube and its direction will be

A) $2mA$ Towards left.

B) $2mA$ Towards right.

C) $1mA$ Towards right.

D) $2mA$ Towards left.

Answer 1

Hint: The velocity with which free electrons get drifted towards the positive end of a conductor that is opposite to the electric field under the influence of an external electric field. When no electric field is applied on a conductor, then the free electrons move due to their thermal velocities.

Complete step by step answer:

Current flowing through a wire or through a hydrogen discharge tube can be defined as the rate of change of electric charge per unit time. It can be mathematically represented as, c

$I = \dfrac{q}{t}$ 

Where $I$ is the current flowing in ampere.

$Q$ is the charge ($c$)

$T$ is the time interval ($s$)

Now, in this question, the total charge will be given by the sum of the charges due to the charges of electrons and protons.

Charge in one electron is, $e = 1.6 \times {10^{ - 19}}C$ 

Charge in one proton is, $p = 1.6 \times {10^{ - 19}}C$

Given, the number of electrons is, ${n_e} = 3.13 \times {10^{15}}$ 

The number of protons is, ${n_p} = 3.12 \times {10^{15}}$ 

Total charge on the discharge tube is given by,

$q = {n_e}e + {n_p}p$ 

Substitute the given values in the above equation, we get 

$ \Rightarrow q = 3.13 \times {10^{15}} \times 1.6 \times {10^{ - 19}}C + 3.12 \times {10^{15}} \times 1.6 \times {10^{ - 19}}C$  

$ \Rightarrow q = {10^{ - 3}}C$ 

Total time, $t = 1s$ 

The current through the discharge tube is given by,

$I = \dfrac{q}{t}$

Substitute the given values in the above equation, we get

$ \Rightarrow I = \dfrac{{{{10}^{ - 3}}}}{1}$

$\Rightarrow I= 1mA$

The total current is $1mA$.

The direction of the flow of current is given as the direction of the positive charges or the opposite direction to the flow of negative charges.

So, the current will flow in the direction of protons that are from left to right.

$\therefore $ The current will be $1mA$ towards the right. The correct option is (C).

Note:

The protons and electrons both have equal and opposite charges. If we know the direction of any one of the charges, that is, anyone of the positive or negative charges, then also we can find the direction of the flow of current.

Protons are positively charged particles whereas electrons are negatively charged particles.