Question
Asked Oct 22, 2019
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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 the figure below.

(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 = 2keλsinθ0/d.


(b) Using your result to part (a), show that the field of a rod of infinite length is E = 2keλ/d.

P
во
-х
о
е-
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P во -х о е-

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Expert Answer

Step 1

Draw the following diagram to represent the electric field at point P due to a small charge particle of length dx, at a distance x from the origin.

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Ex

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Step 2

As the electric field in x direction has equal and opposite magnitude, it cancels and there is no x-component of electric field at point P. Write the expression for y-component of electric field.

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k rdx cos e dE

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Step 3

Write the expression for cos theta and ...

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d cose d cos e x tan e d tan e x d sec2 ede dx

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Electric Charges and Fields

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