x-component y-component A thin rod of length l and uniform charge per unit lengt

Question

x-component y-component A thin rod of length l and uniform charge per unit length ? lies along the x axis as shown in the figure below. Determine the magnitude of the components of the electric field at P, a distance y from the rod along its perpendicular bisector. Suggestion: First, calculate the field at P due to an element of length dx, which has a charge ?dx. Then, change variables from x to ?, using the relationships x = y tan (?) and dx = ysec2 ? d ?, and integrate over ?. (Use k_e for ke, lambda for ?, y for y, and theta_0 for ?0 as necessary.) Using your result to part (a), determine the components of the electric field of a rod of infinite length.

Explanation / Answer

(a)x component =0

y component =2k?(L/(4y^2+L^2)^0.5)/y

(b)x component =0
y component = 2k?/y

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