I want to apologize ahead of time for my apparent inability to get LaTeX to display properly.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

λ = 3.8 x 10^(-6) C/m

R = 32m

r = magnitude of the hypotenuse (the book's convention, a poor choice IMHO)

r = [itex] \sqrt{R^2 + x^2} [/itex]

k = 8.988 x 10^9

P:(0,-32)

cosθ = x/r

a→∞

2. Relevant equations

[itex] dE = λk \int_0^a \frac{dx}{r^2}[/itex]

3. The attempt at a solution

We're supposed to figure out the overall field strength, which is finite.

[itex]dE = λk \int_0^a \frac{dx}{r^2} [/itex]

[itex]dE_x = λk \int_0^a \frac{dx}{r^2} cosθ [/itex]

[itex]dE_x = λk \int_0^a \frac{dx}{r^2} \frac{x}{r}[/itex]

[itex]

dE_x = λk \int_0^a \frac{xdx}{r^3}

[/itex]

[itex]

u = R^2 + x^2 → \frac{du}{2} = xdx

[/itex]

[itex]

dE_x = λk \int_0^a (u)^{-3/2} du

[/itex]

[itex]

dE_x = λk [ -2 u^{-1/2} ]_0^a

[/itex]

[itex]

dE_x = -2λk [ (R^2 + x^2)^{-1/2} ]_0^a

[/itex]

[itex]

dE_x = -2λk [ \frac{1}{\sqrt{R^2 + x^2}} ]_0^a

[/itex]

[itex]

dE_x = -2λk [ \frac{1}{\sqrt{R^2 + \inf^2}} - \frac{1}{\sqrt{R^2}} ]

[/itex]

[itex]

dE_x = -2λk [ 0 - \frac{1}{\sqrt{R^2}} ]

[/itex]

[itex]

dE_x = -2λk [ \frac{1}{R} ]

[/itex]

[itex]

dE_x ≈ -2.13465 x 10^3

[/itex]

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# Homework Help: Finding the net field strength due to a line of charge

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