Electric Field of a Straight Wire at a Particular Distance from Wire

[The Head]

Homework Statement

See attached document

Homework Equations

dE=kdQ/r^2
Ex=Ecos∅

The Attempt at a Solution

dE=kdQ/r^2
E=kλ∫dy/(x^2+y^2) (integrating from y= -L/2 to L/2)
Ex=2kλ∫xdy/(x^2+y^2)^3/2 (change integration to y= 0 to L/2, multiplying expression by 2)

Let y=xtan∅
dy=x(sec∅)^2 d∅

=2kxλ∫x(sec∅)^2/x^3(sec∅)^3 d∅
=2kλ/x∫cos∅ d∅
=2kλ/x(sin∅)
=2kλ/x(sin(arctan(y/x)) (evaluated from y=0 to y=L/2)
=2kλ/x(y/(x^+y^2)^1/2 (evaluated from 0->L/2)
=2kλ/x(L/2)(x^2+(L^2)/4)^.5
=((1.8X10^10)λL/(2x))*(1/x^2+(L^2)/4)^.5)

I would appreciate any help or guidance!

 

[tiny-tim]

Hi The Head!

See attached document

erm …

what attached document? ​

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