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When charged particles move through a hollow conducting cylinder, they change the charge distribution on the surface of the cylinder. So, I was wondering if there would be some resistance against the movement of the charged particles.Partly, also because the change in the surface charge density is not instantaneous.

This thought popped in my mind when I was wondering whether charged particles moving through a hollow conductor interact with the surface charge distribution? By this, I mean would the surface charge density exert a force on the charged particles moving through the conductor?

  • So, to sum it all up, if there were charged particles passing through a hollow conductor, would there be any resistance against their movement? and would the surface charge distribution of a conductor exert a force on the charges. (There is an electric field outside the conductor)
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Yes. Since any conductor has some positive resistivity, and the image charge is thereby generating heat, energy must be taken from the particle.

(To be exact, for the theoretical limit of a perfect superconductor with the appropriate initial conditions, the image charge could be level with the particle and therefore not slow it down...or, with any other initial condition, there would be velocity-oscillations.)

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  • $\begingroup$ So, the kinetic energy of the particle would be converted into heat? What does this rate of decrease in kinetic energy be for conductors like copper? negligible? and what does is dependent on, the particles velocity? This happens for particles travelling in the hollow cavity of the conductor right?Thanks $\endgroup$ – Chandrahas Feb 10 '17 at 4:12
  • $\begingroup$ If I keep passing a positively charged particle beam through the conductor, since the charge distribution in the hollow cavity doesn't change, there would also be no change in the surface charge distribution. Hence, there wouldn't be any heating effect. But it would happen due to the magnetic field initially, but then the system would attain equilibrium. So, does this mean that there would be no heating effect after a certain period of time? $\endgroup$ – Chandrahas Feb 10 '17 at 4:25
  • $\begingroup$ once a steady state is established no further parasitic currents flow and the apparent resistance stops. $\endgroup$ – Floris Feb 10 '17 at 4:32
  • $\begingroup$ Yes, the kinetic energy goes to heat. At some low velocity, yes, it will be negligible. You can calculate the energy loss from the image charge's current for copper's resistivity, including skin effects, and see that yes, the energy loss rate is greater at a higher particle velocity. Floris answered your beam question. $\endgroup$ – bobuhito Feb 10 '17 at 4:35

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