Line of charge, Feild on the origin

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Homework Help Overview

The problem involves calculating the electric field created by a line of charge with a uniform density along a specified segment. The line of charge is positioned at a certain distance from the origin, and the task is to determine the electric field at that point, including its x- and y-components.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need for integration to find the electric field due to a continuous charge distribution, questioning the correct setup for the integral and the expressions for the electric field components.

Discussion Status

The discussion is ongoing, with participants exploring various approaches to set up the integral for calculating the electric field. Some have provided guidance on expressing the differential electric fields and the need to consider the geometry of the problem. There is a recognition of confusion regarding the integration process and the expressions used.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may impose specific rules on the methods and approaches they can use. There is also uncertainty about whether integration is required or if derived formulas can be applied directly.

  • #31
Yeah it is.
 
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  • #32
I'm having trouble completing the integral. I get this far:

dE_x = \frac{\lambda x}{4 \pi \epsilon (x^2 + y^2)} dx
 
  • #33
That expression is incorrect. What is r(x)^2 * sqrt(x^2+y^2)?
 
  • #34
(x^2 + y^2) * \sqrt{x^2 + y^2} = x^2 \sqrt{x^2 + y^2} + y^2 \sqrt{x^2 + y^2}<br />
 
  • #35
Or you make it a lot easier by writing it as (x^2 + y^2)^{3/2}. To integrate you may need to do a trigo substitution.
 

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