Algebra of two equal positive charges

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SUMMARY

The discussion focuses on calculating the electric field produced by two equal positive charges located on the y-axis at positions y = +a and y = -a. The electric field on the x-axis is defined as Ex = 2kqx(x² + a²)⁻³/². Near the origin, when x is significantly smaller than a, the electric field approximates to Ex ≈ 2kqx/a³. For values of x much larger than a, the electric field simplifies to Ex ≈ 2kq/x², which aligns with the expected behavior of electric fields from point charges.

PREREQUISITES
  • Understanding of Coulomb's Law and electric fields
  • Familiarity with vector calculus and field lines
  • Knowledge of limits and approximations in physics
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of electric fields from point charges using Coulomb's Law
  • Explore the concept of electric field lines and their representation
  • Learn about the superposition principle in electrostatics
  • Investigate the behavior of electric fields at various distances from point charges
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Physics students, electrical engineers, and anyone interested in electrostatics and electric field calculations.

Lisa...
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I need some help in finding a way to solve the following problems.:

- Two equal positive charges q are on the y axis, one at y= +a and the other at y= -a.

a) Show that the electric field on the x-axis is along the x-axis with
Ex= 2kqx(x2 + a2)-3/2.

b) Show that near the origin, when the x is much smaller than a, Ex is approximately 2kqx/a3.

c) Show that for values of x much larger than a, Ex is approximately 2kq/x2. Explain why you would expect this result even before calculating it.

Thanks for your efforts!
 
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