Flux Through Face of Tetrahedron

In summary, the flux through another face of a regular tetrahedron when a point charge is placed on one of the faces can be calculated by dividing the total charge by six times the permittivity. This is because half of the total flux does not go through the tetrahedron, and the remaining half is equally shared among the three remaining faces. This calculation assumes that the point charge is placed at the center of one of the faces.
  • #1
physicsphreak2
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Homework Statement


Suppose a point charge is placed on the face of a regular tetrahedron. What is the flux through another one of the faces?


Homework Equations





The Attempt at a Solution


I know that if the charge is placed at the center of the tetrahedron, the flux through any face would simply be q/(4*ε) since each face gets an equal share of the total flux.

But since the charge is placed on one of the faces, I would think that each other face sees q/(6*ε) of flux? Since "half the total flux" simply doesn't go through the tetrahedron at all, and the half that does is shared equally with a third going to each remaining face?

Is this valid?
 
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  • #2
That sounds right to me as long as the point charge is placed at the center of one of the faces.
 
  • #3
Definitely yes.
 

1. What is the charge on the face of a tetrahedron?

The charge on the face of a tetrahedron depends on the distribution of charges on the vertices of the tetrahedron. It can be positive, negative, or neutral depending on the net charge of the vertices.

2. How is the charge distributed on the face of a tetrahedron?

The charge on the face of a tetrahedron is evenly distributed among the three vertices that make up the face. This means that each vertex contributes an equal amount of charge to the face.

3. Can the charge on the face of a tetrahedron be zero?

Yes, the charge on the face of a tetrahedron can be zero if the charges on the vertices cancel each other out. For example, if one vertex has a positive charge and the other three have negative charges of the same magnitude, the net charge on the face will be zero.

4. How does the angle between two faces of a tetrahedron affect the charge on the face?

The angle between two faces of a tetrahedron does not affect the charge on the face. The charge on the face only depends on the charges on the vertices and their distribution.

5. How is the charge on the face of a tetrahedron related to its overall charge?

The charge on the face of a tetrahedron is a fraction of the overall charge of the tetrahedron. The exact fraction depends on the number of vertices and their individual charges. If the tetrahedron has a net charge of Q, the charge on each face is Q/4.

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