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Question: In a hydrogen tube it is observed that through a given cross-section \(3.13\times {{10}^{15}}\) elec...

In a hydrogen tube it is observed that through a given cross-section 3.13×10153.13\times {{10}^{15}} electrons are moving from right to left and 3.12×10153.12\times {{10}^{15}} protons are moving from left to right. What is the electric current in the discharge tube and what is the direction?
A. 1 mA towards right
B. 1 mA towards left
C. 2 mA towards left
D. 2 mA towards right

Explanation

Solution

Hint: obtain the equation of current. Find the total charge flowing through the system in unit time and put them in the equation to find the current. To find the direction look for the direction of the positive charges.
Complete step by step solution: Current flowing through a wire or through the discharge tube can be defined as the rate of change of electric charge per unit time. It can be mathematically expressed as,
I=qtI=\dfrac{q}{t}
Where, I is the current flowing in ampere, q is the charge flowing in coulomb and t is the time.
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=1.6×10−19Ce=1.6\times {{10}^{-19}}C
Charge in one proton is p=1.6×10−19Cp=1.6\times {{10}^{-19}}C
Given the number of electrons is ne=3.13×1015{{n}_{e}}=3.13\times {{10}^{15}}
The number of protons is np=3.12×1015{{n}_{p}}=3.12\times {{10}^{15}}
Total charge on the discharge tube is
q=nee+npp q=3.13×1015×1.6×10−19C+3.12×1015×1.6×10−19C q=10−3C \begin{aligned} & q={{n}_{e}}e+{{n}_{p}}p \\\ & 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 \\\ & q={{10}^{-3}}C \\\ \end{aligned}
Total time is, t=1st=1s
The current through the discharge tube is,
I=qt I=10−31A I=1mA \begin{aligned} & I=\dfrac{q}{t} \\\ & I=\dfrac{{{10}^{-3}}}{1}A \\\ & I=1mA \\\ \end{aligned}
The total current is 1 mA.
The direction of 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.
So, the current will be 1 mA towards the right.
The correct option is (A).
Note: the proton and electron both have equal and opposite charges. If we know the direction of any one of the charges i.e. any one of the positive or negative charges, then also we can find the direction of flow of current.