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An infinitesimal length dx of rod has dq= dx of charge, where =Q/L.

A thin rod of length L with total charge Q lies along the x-axis as shown. Find the magnitude and direction of the electric field at P, a distance y from the rod and along the perpendicular bisector of the rod. An infinitesimal length dx of rod has dq= dx of charge, where =Q/L. y.

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An infinitesimal length dx of rod has dq= dx of charge, where =Q/L.

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  1. A thin rod of length L with total charge Q lies along the x-axis as shown. Find the magnitude and direction of the electric field at P, a distance y from the rod and along the perpendicular bisector of the rod. An infinitesimal length dx of rod has dq=dx of charge, where =Q/L. y Ex from a dq of charge with x=|x1|>0 will be equal and magnitude and opposite in direction to Ex from a dq of charge with x=-|x1|<0. P y x dq dq Thus, by symmetry, Ex,net=0. L

  2. dE  y P  r y x dq L

  3. Limits of integration are from 0 to 1, where dE  y P  r y x dq L

  4. because sin=-sin(-) dE  y You can substitute for sin(1) if you want: P  r y x dq L

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