A thin rod carries charge Q distributed uniformly over its length L and is situated on the x-axis between x ±L/2.(a) Find the electric field at an arbitrary point (x, y).(You’ll have to do separate integrals for the x- and y-components.) (b) Show that your result reduces to that of Problem 72 when x =0 and to that of Problem 57 when y =0 and x > L/2.

Data from Problem 57

A thin rod lies on the x-axis between x =0 and x =L and carries total charge Q distributed uniformly over its length. Show that the electric field strength for x = 7L is given by E= KQ/[x(x-L)].

Data from Problem 72

Figure 20.34 shows a thin rod of length L carrying charge Q distributed uniformly over its length.
(a) What’s the line charge density on the rod? 

(b) Modify the calculation of Example 20.7 to find an expression for the electric field at a point P a distance y along the perpendicular bisector. 

(c) Show that your result reduces the the field of a point charge when |y|>>L.