Electron Lens An electrostatic electron lens consists of a thin, charged, hollow cylinder of radius R...

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Electron Lens An electrostatic electron lens consists of a thin, charged, hollow cylinder of radius R and length L. The center is at the origin and the cylinder axis coincides with the r3 axis. The negative charge -Q is evenly distributed over the entire surface. a) Determine the electric field Ei(0, 0, r3) along the cylinder axis. (15p) 13 b) Compute the field Ei(r1,0,0) for short lenses with L << R near the origin with r1 << R to first order. Show that it has a stabilizing effect in the r1 direction, i.e. it pulls electrons back into the center. Electron Lens An electrostatic electron lens consists of a thin, charged, hollow cylinder of radius R and length L. The center is at the origin and the cylinder axis coincides with the r3 axis. The negative charge -Q is evenly distributed over the entire surface. a) Determine the electric field Ei(0, 0, r3) along the cylinder axis. (15p) 13 b) Compute the field Ei(r1,0,0) for short lenses with L << R near the origin with r1 << R to first order. Show that it has a stabilizing effect in the r1 direction, i.e. it pulls electrons back into the center.

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a Consider a point P placed outside the spherical shell Here ... View the full answer