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].
