Master Electromagnetism on the GRE with Problem 55 Explained

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SUMMARY

The discussion centers on GRE problem 55, which involves understanding the interference of electromagnetic (EM) fields. The correct answer is confirmed to be (A), despite initial confusion suggesting (C) due to the perpendicular nature of the two EM fields. The resultant electric field is expressed as ##\mathbf E(t) = \hat x E_1 \cos(\omega t + \phi) + \hat y E_2 \cos(\omega t + \phi)##, where ##\omega## and ##\phi## are constants. The key takeaway is the importance of recognizing the phase relationship and vector addition in determining the resultant field.

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  • Understanding of electromagnetic wave theory
  • Familiarity with vector calculus
  • Knowledge of phase relationships in wave interference
  • Basic proficiency in GRE physics problem-solving techniques
NEXT STEPS
  • Study the principles of electromagnetic interference in depth
  • Learn about vector addition of electric fields in physics
  • Review GRE physics problem-solving strategies
  • Explore the mathematical representation of wave functions
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Students preparing for the GRE, particularly those focusing on physics, educators teaching electromagnetism, and anyone seeking to enhance their understanding of wave interference concepts.

Silviu
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Hello! I have a question about a GRE problem. It is problem 55 in the attached file. So the answer seems to be (A) but I am a bit confused. Isn't this basically interference, so the right answer would be (C)?
 

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Remember that the two EM fields are perpendicular to each other. Since after the mentioned OPD the waves are in phase, the resultant field at that point in space will be ##\mathbf E(t) = \hat x E_1 \cos(\omega t + \phi) + \hat y E_2 \cos(\omega t + \phi)## where ##\omega## and ##\phi## are constants. What is the length of this vector?
 
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