- #1

Ahmed A

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## Homework Statement

A straight nonconducting plastic wire 8.50 cm long carries a charge density of +175 nC/m distributed uniformly along its length. It is lying on a horizontal table top. Find the magnitude and direction of the electric field this wire produces at a point 6.00 cm directly above its midpoint.

## Homework Equations

E = [itex]\frac{1}{4πε_0}[/itex] * [itex]\frac{Q}{r^2}[/itex]

λ = 175 nC/m

a = 4.25 cm

y = 6.00 cm

## The Attempt at a Solution

I made a diagram with the rod along the x-axis, with the y-axis intersecting it at the center. The endpoints of the rod are ±a where a=4.25cm.

dE = [itex]\frac{1}{4πε_0}[/itex] * [itex]\frac{λdx}{x^2+y^2}[/itex]

dE

_{y}= dE sin(θ)

sin(θ) = [itex]\frac{y}{\sqrt{x^2+y^2}}[/itex]

dE

_{y}= [itex]\frac{λy}{4πε_0}[/itex] * [itex]\frac{dx}{(x^2+y^2)^\frac{3}{2}}[/itex]

E

_{y}= [itex]\frac{λy}{4πε_0}[/itex] * [itex]\int^{a}_{-a} \frac{dx}{(x^2+y^2)^\frac{3}{2}}[/itex]

E

_{y}= [itex]\frac{λa}{2πε_{0}y\sqrt{x^2+y^2}}[/itex]

The result I got after plugging all the numbers in is E = 3.03 * 10

^{4}N/C but other sources online say the correct answer is 4.28 * 10

^{4}N/C. What did I do wrong?

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