Continuous Charge Distributions

[WarpSpeedo]

Homework Statement

A charge lies on a string that is stretched along an x-axis from x = 0 to x = 3.00 m; the charge density on the string is a uniform 9.00 nC/m. Determine the magnitude of the electric field at x = 8.00 m on the x axis.

Homework Equations

$\int_0^3 kλ/(8-x)^2\,dx$

The Attempt at a Solution

k=8.99e9
λ=9

I know k and λ can come out of the integral leaving 1/(8-x^2). which gives me 9.44e-10 which webassign marks wrong.

 

[vela]

Your set-up looks fine, but I don't get anything close to the numerical answer you're getting.

 

[TSny]

The Attempt at a Solution

k=8.99e9
λ=9

I know k and λ can come out of the integral leaving 1/(8-x^2). which gives me 9.44e-10 which webassign marks wrong.

Are you thinking about the units for λ?

 

[WarpSpeedo]

Problem was the units for λ. Thanks for your help

 

[HalfLostAndSearching]

I would like to point out that the attempted solution is missing the units for the charge density (nC/m). Additionally, the integral should be taken from x=0 to x=8.00 m, as the electric field at x=8.00 m is influenced by the entire length of the string. Furthermore, the attempted solution does not take into account the fact that the charge distribution on the string is continuous, meaning that the charge is not just located at specific points but is spread out along the entire length of the string. To properly solve this problem, one would need to use the formula for the electric field due to a continuous charge distribution, which takes into account the charge density and the distance from the point of interest. It is always important to carefully consider the given information and use the appropriate equations and units when solving scientific problems.