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In my study book of radio frequency engineering is a question, which is pretty odd in my opinion.

Calculate the electrical field of a cathode ray for the cases r < d and r > d. There are two following conditions.

  • Velocity as a function of radius $$ v_z =v_0 \cdot [1 - (\frac{r}{d})^3]$$
  • Charge density $$ \rho = \rho_0 \cdot [ 1 + (\frac{r}{d})^2]$$

Can anyone tell my how to get to this conditions? There are no other mentions about them in this book. I tried to calculate the E-field with $$E = \frac{\rho}{2 \cdot \pi \cdot \epsilon \cdot r}$$ but i cannot figure out, how to get a proper solution.

PS: I don't know which radius and what's meant with d. I hoped one of you can help me, maybe there's a known similar example.

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  • \$\begingroup\$ What are \$ r \$ and \$ d \$? Was there a diagram in the book? "Radius"? What radius? Put the information into your question rather than in the comments. \$\endgroup\$ – Transistor Feb 7 '18 at 22:54
  • \$\begingroup\$ My guess would be d is the distance between cathode and anode. \$\endgroup\$ – Janka Feb 8 '18 at 1:01
  • \$\begingroup\$ Stick your head inside a CRT tube, and let us know... \$\endgroup\$ – Sparky256 Feb 8 '18 at 1:57

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