The potential at a point P, a distance a above one end of a uniformly charged rod of length ℓ, lying along the x axis is,

Use this result to derive an expression for the y component of the electric field at P.

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James SamasLv8

22 Nov 2020

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A thin rod of length ℓ and a 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,

amethysthound558

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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.

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azureweasel81

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Textbook Problem

A thin rod of length ℓ and a 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.