Question

In a particular television tube, a beam of electrons is emitted. The beam current is $80\mu A$. How many electrons strike the screen of TV every second? Also find the total charge striking the screen in 2minutes?

Answer 1

Hint: As we know that current is directly proportional to the charge and inversely proportional to the time.
$I = \dfrac{q}{t}$
Where $I$= current
And $t$ = time
In this, we need to find the value of charge, as current and time is given in this question. By substituting all these two values, we can determine the charge value.

Complete Step by step answer: Given: Beam current = $80\mu A$=$80 \times {10^{ - 6}}A$
Time = 2minutes = $2 \times 60\sec $= $120s$
Let’s calculate the number of electrons striking per second is beam current per second:
Current is charge flowing through the conductor per unit second. Current is rate quantity. The SI unit of current is Ampere.
$I = \dfrac{q}{t}$………………………………………………………………………………………... (I)
Where $I$= current
And $t$ = time
But charge flowing for a unit second is given by charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charge: positive and negative. Like charges repel each other and the same charges attract each other. SI unit of charge is coulomb.
$q = I \times e$ ……………………………………………………………………………………. (II)
$\Rightarrow q = 80 \times {10^{ - 6}} \times 1.6 \times {10^{ - 19}}$
$\Rightarrow q = 128 \times {10^{ - 25}}$
$\Rightarrow q = 1.28 \times {10^{ - 23}}C$
Hence current flowing through any conductor is always proportional to the charge in that conductor and inversely proportional to the time taken to flow that charge.
In two minutes the charge flowing is given by-
$q = It$
$\Rightarrow q = 80 \times {10^{ - 6}} \times 120$
$\Rightarrow q = 9.6 \times {10^{ - 3}}C$

Hence charge flowing for two minutes =$q = 9.6 \times {10^{ - 3}}C$

Note: Current is charge flowing through conductor per unit second. Current is rate quantity. The SI unit of current is Ampere.
And charge flowing for a unit second is given by charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charge: positive and negative. Like charges repel each other and the same charges attract each other. SI unit of charge is coulomb. It is given by: $q = I \times e$