1. 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
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 L
Thus, by symmetry, Ex,net=0.

2. dE  y P  r y x dq L

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

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