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Given a thin, straight rod of length L lying on the x axis, extending from the...

Given a thin, straight rod of length L lying on the x axis, extending from the originx=0 to x=L. The rod carries total charge +Q uniformly distributed over its length. We want to find the net electric field E du to this rod at point P (b,0) on the x axis, with b>L (that means P lies outside (“to the right of”) the rod. Again, let’s do it step-by-step—

  1. (a) Sketch the setup.

  2. (b) At an arbitrary location x somewhere along the rod (0<x<L) pick an infinitesimal slice dx. In

    terms of Q, L, and dx how much charge (call it dq) does that slice carry?

  3. (c) Write an expression for the electric field (call it dE) at point P due to just that infinitesimal

    charge dq (which you may assume to be a point charge).

  4. (d) Now do an integral to find the net E at P due to the entire rod. (Remember, E is a vector!)

  5. (e) Show that if P is very far from the rod (b>>L) your result of part (d) simplifies to an expression

    that should look familiar. (In other words, what does that rod look like when viewed from very far away?)

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