Line of charge, Feild on the origin

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SUMMARY

The discussion focuses on calculating the electric field generated by a finite line of charge with a uniform density of 35.0 nC/m, positioned along the line y = -12.6 cm, from x = 0 to x = 44.2 cm. Participants emphasize the need for integration to derive the electric field components at the origin, specifically addressing the expressions for dE_x and dE_y. The correct approach involves using the relationship dE = (λ dx)/(4πε r(x)^2) and integrating with respect to x, while expressing cos(θ) and sin(θ) in terms of x and y. The final expressions for E_x and E_y must be evaluated numerically over the specified limits.

PREREQUISITES
  • Understanding of electric fields due to continuous charge distributions
  • Familiarity with integration techniques in calculus
  • Knowledge of trigonometric functions and their applications in physics
  • Proficiency in using the formula for electric fields: E = kQ/r² for point charges
NEXT STEPS
  • Study the integration of electric fields from continuous charge distributions
  • Learn how to derive electric field components using trigonometric relationships
  • Explore the application of the formula E = (λ dx)/(4πε r²) in various geometrical configurations
  • Review examples of electric fields from finite line charges and their calculations
USEFUL FOR

Students in physics, particularly those studying electromagnetism, as well as educators and anyone involved in teaching or learning about electric fields and charge distributions.

  • #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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