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A thin rod of length ℓ and uniform charge per unit length 3 lies along the x axis, as shown in Figure P23.35.
(a) Show that the electric field at P, a distance y from the rod along its perpendicular bisector, has no x component and is given by E = 2ke3 sin +0/y.
(b) What If? Using your result to part (a), show that the field of a rod of infinite length is E = 2keA/y. (Suggestion: First calculate the field at P due to an element of length dx, which has a charge 3 dx. Then change variables from x to +, using the relationships x = y tan θ and dx = y sec2 θ d θ, and integrate over θ.)
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