What is the Current Generated by a Single Electron in Uniform Circular Motion?

In summary, the average current of a single electron in uniform circular motion can be found by taking the absolute value of e multiplied by the angular speed divided by 2π. Using this formula, the current is evaluated to be 5.1 x 10^-4 A when the angular speed is 2 x 10^16 rad/s and the radius is 5 nm. The current is in the counterclockwise direction.
  • #1
tony873004
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A single electron in uniform circular motion constitutes an average current around the circle. If the electron moves clockwise with angular speed in a circle of radius r, find the current. Evaluate I if [tex]\omega=2X10^{16}[/tex] rad/s and r = 5 nm.

I never used radius r in my answer. This book usually doesn't thrown in irrelavant information in the questions. Did I do this right?

[tex]\begin{array}{l}
I = \left| {\frac{Q}{t}} \right| \\
\\
t = \frac{d}{v} = \frac{{2\pi }}{\omega } \\
\\
I = \left| {\frac{Q}{{\left( {\frac{{2\pi }}{\omega }} \right)}}} \right| = \left| {\frac{{Q\omega }}{{2\pi }}} \right| = \left| {\frac{{ - e\omega }}{{2\pi }}} \right| = \frac{{e\omega }}{{2\pi }} \\
\\
\frac{{1.602 \times 10^{ - 19} {\rm{C}} \times 2 \times 10^{16} {\rm{rad/s}}}}{{2\pi }} = 5.1 \times 10^{ - 4} {\rm{C/s = }}5.1 \times 10^{ - 4} {\rm{A}} \\
\end{array}[/tex]

 
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  • #2
Right. The current would be in the CCW direction. (I haven't checked the arithmetical calculation.)
 
  • #3
Thanks for verifying that, and reminding me to include direction.
 

Related to What is the Current Generated by a Single Electron in Uniform Circular Motion?

1. What is electron current and how is it related to electricity?

Electron current refers to the movement of electrons through a conductor, which is the basis of electricity. When electrons flow through a conductor, they create a flow of electric charge, which can be harnessed to power devices and machines.

2. How is electron current measured?

Electron current is measured in amperes (A), which is a unit of electric current. The amount of electrons flowing through a conductor per second is measured to determine the current.

3. What factors affect the flow of electron current?

The flow of electron current can be affected by the type of conductor, the temperature, and the presence of any resistance in the circuit. The material, thickness, and length of the conductor can also impact electron flow.

4. What is the relationship between voltage and electron current?

Voltage is the force that drives electrons to flow through a conductor. The higher the voltage, the more electrons will flow through the conductor, resulting in a higher electron current. This relationship follows Ohm's Law, which states that current is directly proportional to voltage.

5. How is electron current used in everyday life?

Electron current is used in countless everyday devices, such as light bulbs, computers, and phones. It is also used in power grids to distribute electricity to homes and businesses. Additionally, electron current is used in medical equipment, transportation systems, and many other essential technologies.

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