Calculating Electric Flux on Hemispherical Surface | Gauss' Law Solution

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SUMMARY

The discussion focuses on calculating electric flux through a hemispherical surface using Gauss' Law. For a uniform electric field E = E0 khat, the flux through the open hemispherical surface is determined by the orientation of the electric field relative to the surface normal. When the electric field is E = E0 ihat, the dot product with khat results in zero, confirming that the electric flux is indeed zero due to the perpendicular nature of the field lines to the surface.

PREREQUISITES
  • Understanding of Gauss' Law
  • Familiarity with electric fields and their representations
  • Knowledge of vector dot products
  • Concept of surface normals in physics
NEXT STEPS
  • Review the application of Gauss' Law in different geometries
  • Study vector calculus, focusing on dot products and their physical implications
  • Explore electric field calculations for various configurations
  • Investigate the relationship between electric flux and surface area
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Students studying electromagnetism, physics educators, and anyone interested in applying Gauss' Law to solve problems related to electric fields and flux calculations.

uchicago2012
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Homework Statement


(a) Calculate the electric flux through the hemispherical surface shown in the figure. (The surface is an open shell, with no bottom.) The electric field is uniform: E = E0 khat.
(b) If the electric field is instead E = E0 ihat, what is the flux?

Homework Equations


Gauss' Law

The Attempt at a Solution


I was just wondering, for b), since ihat dot khat = 0, does that mean the electric flux is zero? Because it seems like the electric flux will always be perpendicular to the normal force if it is E = E0 khat
 

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the net field lines entering the surface are sae as not lines coming out so yes flux will be 0
 

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