Magnitude of electric field due to line of charge

AI Thread Summary
To determine the electric field at x = 5.5 m due to a line of charge with a uniform linear density of 9.4 nC/m, the correct approach involves recognizing that the distance r varies with the position of each infinitesimal charge element dq along the line. The expression for the electric field should account for this variation, specifically using r = (5.5 - x) for each charge element. The initial attempt incorrectly assumed a constant r, leading to an incorrect calculation of the electric field. Proper integration from x = 0 to x = 3 m is necessary to accurately compute the total electric field. Understanding how r changes with respect to x is crucial for solving this problem correctly.
CentreShifter
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Homework Statement



A charge (uniform linear density = 9.4 nC/m) lies on a string that is stretched along an x-axis from x = 0 to x = 3.0 m. Determine the magnitude of the electric field at x = 5.5 m on the x axis.


Homework Equations



\stackrel{\rightarrow}{dE}=\frac{\lambda dx}{4 \pi \epsilon_{0} r^2}\hat{r}

The Attempt at a Solution



I believe the unit vector can eliminated since the point is on the same axis as the line of charge (cos(0)=1). My concern is with my limits of integration and with my "r" argument. My final expression was:

E = \frac{\lambda}{4 \pi \epsilon_{0} 5.5^2} \int^{3}_{0} dx which got me an 8.38244 N/C, a wrong answer.
 
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Looks like your r is a function of x.

For any dq isn't r = (5.5 - x) ?
 
Yes! I knew the influence of dq would vary with distance from it. I just wasn't sure how to incorporate that. I guess I'm having trouble visualizing r as a function of x that way. Is the x in (5.5 - x) the position of dq?
 
CentreShifter said:
Yes! I knew the influence of dq would vary with distance from it. I just wasn't sure how to incorporate that. I guess I'm having trouble visualizing r as a function of x that way. Is the x in (5.5 - x) the position of dq?

As I see it, yes. That should be the r for a particular dq located at x, and relative to the point 5.5.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

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