Angle of electric field line heading to infinity

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SUMMARY

The discussion focuses on determining the angle at which electric field lines originating from a charge of 2q at x=0 head towards infinity, while also addressing the point on the x-axis where the electric field is zero. The solution for the zero electric field point is established as x = a(2 + sqrt(2)). The challenge lies in calculating the angle of the field lines that delineate those heading to infinity versus those terminating at the charge -q located at x=a.

PREREQUISITES
  • Understanding of electric field concepts and field line behavior
  • Familiarity with Coulomb's Law and electric field equations
  • Basic knowledge of geometry and trigonometry for angle calculations
  • Ability to sketch electric field lines based on charge distributions
NEXT STEPS
  • Study the derivation of electric field lines for point charges
  • Learn about the concept of equipotential surfaces in electrostatics
  • Explore the mathematical techniques for solving electric field problems involving multiple charges
  • Investigate the implications of field line behavior in different charge configurations
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in electrostatics, particularly those studying electric fields and charge interactions in advanced high school or undergraduate courses.

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Homework Statement


Charges 2q and -q are located on the x-axis at x=0 and x=a respectively.

(a) Find the point on the x-axis where the electric field is zero, and make a rough sketch of some field lines.

(b) You should find that some of the field lines that start on the 2q charge end up on the -q charge, while others head off to infinity. Consider the field lines that form the cutoff between these two cases. At what angle (with respect to the x axis) do these lines leave the 2q charge?

Homework Equations


E = 1/(4*pi*e0) q^2/r^2

The Attempt at a Solution



I found the solution for part (a) to be x = a(2 + sqrt(2)), but part (b) has me stumped and I'm not really sure how to approach it. Any pointers in the right direction would be greatly appreciated.
 
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