Calculate the electric current flowing in one revolution of an electron moving in its orbit at a rate of [tex][tex]$68 \times 10^{15}$[/tex][/tex] rounds per second. The charge on an electron is [tex][tex]$1.6 \times 10^{-19} C$[/tex][/tex].



Answer :

Sure, let's solve the given problem step by step.

Given data:

- Charge on an electron, [tex]\( Q = 1.6 \times 10^{-19} \)[/tex] Coulombs
- Frequency of the electron's movement, [tex]\( f = 68 \times 10^{15} \)[/tex] revolutions per second

To find:
The electric current flowing in one revolution.

Explanation:

Electric current ([tex]\( I \)[/tex]) is defined as the rate of flow of electric charge. Mathematically, it can be expressed as:

[tex]\[ I = Q \times f \][/tex]

where:
- [tex]\( I \)[/tex] is the electric current in Amperes (A)
- [tex]\( Q \)[/tex] is the charge in Coulombs (C)
- [tex]\( f \)[/tex] is the frequency in revolutions per second (Hz)

Calculation:

Now we will substitute the given values into the formula:

[tex]\[ I = (1.6 \times 10^{-19} \, \text{C}) \times (68 \times 10^{15} \, \text{Hz}) \][/tex]

Simplify:

Multiply the numerical values first:

[tex]\[ 1.6 \times 68 = 108.8 \][/tex]

Next, multiply the powers of 10:

[tex]\[ 10^{-19} \times 10^{15} = 10^{-4} \][/tex]

Therefore, combining these, we get:

[tex]\[ I = 108.8 \times 10^{-4} \][/tex]

This can be simplified further to:

[tex]\[ I = 1.088 \times 10^{-2} \, \text{A} \][/tex]

Converting to a more familiar unit:

[tex]\[ 1.088 \times 10^{-2} \, \text{A} = 0.01088 \, \text{A} \][/tex]

Conclusion:

The electric current flowing in one revolution of the electron is [tex]\( 0.01088 \, \text{A} \)[/tex].