A thin rod of length ℓ and uniform charge per unit length λ lies along the x axis as shown in Figure P23.8. (a) Show that the electric field at P, a distance d from the rod along its perpendicular bisector, has no x component and is given by E = 2kλ sin θ0 /d. (b) What If? Using your result to part (a), show that the field of a rod of infinite length is E = 2kλ/d. Figure P23.8

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Chapter3: Vectors
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A thin rod of length ℓ and uniform charge per unit length λ lies along the x axis as
shown in Figure P23.8. (a) Show that the electric field at P, a distance d from the rod
along its perpendicular bisector, has no x component and is given by E = 2kλ sin θ0
/d.
(b) What If? Using your result to part (a), show that the field of a rod of infinite length
is E = 2kλ/d.
Figure P23.8

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why do the value of r= sqr d^2+(x-l/2)^2, where does l/2 comes from? explain please. if you can make a free body diagram please.

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