Question
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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.

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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.

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.

Step 3

Write the expression for cos theta and ...

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### Electric Charges and Fields 