Unravelling Electric Flux: Area Vector and E-Field Vector

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SUMMARY

The discussion focuses on the concept of electric flux, specifically how it is calculated using the dot product of the area vector and the electric field vector. The area vector is defined as perpendicular to the surface, which is essential for accurately determining the flux through a surface. The relationship between the area and the electric field is clarified by noting that the scalar flux is influenced by both the area and the angle between the area vector and the electric field direction. This understanding is crucial for solving problems related to electric flux in physics.

PREREQUISITES
  • Understanding of electric flux and its mathematical representation
  • Familiarity with vector operations, specifically the dot product
  • Knowledge of the relationship between area and surface normals
  • Basic principles of electromagnetism, including electric fields
NEXT STEPS
  • Study the mathematical derivation of electric flux using the formula φ = EA cos(θ)
  • Explore the concept of magnetic flux and its similarities to electric flux
  • Learn about the application of Gauss's Law in calculating electric fields
  • Investigate the role of surface orientation in electromagnetic theory
USEFUL FOR

Students of physics, educators teaching electromagnetism, and anyone interested in understanding the principles of electric flux and its applications in real-world scenarios.

anonymousphys
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1. When solving for electric flux, we dot product the area vector and the e-field vector. Why does area have a vector, and why is it perpendicular to the surface?

Homework Equations


phi=EA

The Attempt at a Solution


Isn't area scalar; Is it because we just want to simplify the calculations so we "imagine" it to be vector?

Thanks for any replies.
 
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Welcome to PF!

anonymousphys said:
1. When solving for magnetic flux, we dot product the area vector and the e-field vector. Why does area have a vector, and why is it perpendicular to the surface?

Isn't area scalar; Is it because we just want to simplify the calculations so we "imagine" it to be vector?

Hi anonymousphys! Welcome to PF! :smile:

Basically for the same reason that to find the angle between two planes, we actually find the angle between their normals.

(Scalar) flux is the amount of a vector field going through a surface.

It's proportional to area, but it also depends on the angle the area presents to the field direction.

Imagine a "tube" of flux … the flux through any surface cutting that tube will be the same, but if the surface is angled, the surface area will be larger by an amount (in the limit) equal to 1/cosine of the angle, so we have to multiply the area by the cosine first to keep the result the same for all angles.
 

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