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

[tony873004]

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 $$\omega=2X10^{16}$$ 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?

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

 

[Shooting Star]

Right. The current would be in the CCW direction. (I haven't checked the arithmetical calculation.)

 

[tony873004]

Thanks for verifying that, and reminding me to include direction.