Electrostatics - Coulomb's Law

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SUMMARY

The discussion centers on the derivation of the cosine term in the electric field formula, specifically in the context of example 2.1 from Griffith's Electrodynamics. The contributor clarifies that the term cos(theta) arises from the relationship between the unit vector r_hat and the z-axis, leading to the expression 2cos(theta)z_hat. This highlights the importance of understanding vector components in electrostatics, particularly when applying Coulomb's Law.

PREREQUISITES
  • Understanding of vector calculus and unit vectors
  • Familiarity with Coulomb's Law and electrostatic principles
  • Basic knowledge of Griffith's Electrodynamics, specifically example 2.1
  • Concept of electric field (E) and its vector representation
NEXT STEPS
  • Study the derivation of electric field formulas in Griffith's Electrodynamics
  • Learn about vector components and their applications in physics
  • Explore the implications of Coulomb's Law in different coordinate systems
  • Review examples involving unit vectors in electrostatics
USEFUL FOR

Students of physics, particularly those studying electromagnetism, educators teaching electrostatics, and anyone seeking a deeper understanding of vector analysis in electric fields.

jinksys
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I'm doing example 2.1 in Griffith's Electrodynamics book. Can someone explain where the cos(theta) comes from in the formula for dE? The formula is on the first image: Here.
 
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SOLVED:

I see what's going on. If you add the r_hat vectors you end up with 2(z/r)z_hat. z/r=cos(theta). So we end up with 2cos(theta)z_hat.
 
that looks so hard. are you supposed to figure out that formula all by yourself
 
bael said:
that looks so hard. are you supposed to figure out that formula all by yourself

No, the formula is given to you in a general form.
 

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