  #  It is often simpler to find the flux through one surface of an object than through another.  In the case of the cone the flux through the base  (Area = R2) is the same as the flux through the lateral surface, but it is much easier to calculate the flux through the base. = E Alateral cos = E ( R2)

 Q:     If the electric field in a point P in space is zero, does this mean that there are no charges in the vicinity of point P? A:    No, it may just be that the individual fields created by individual charges cancel each other at point P. Q:     Why does excess charge on an isolated conductor reside on the conductor's surface? A:    Any solid object is a crystal.  The total energy of a crystal can be calculated at any point of the solid.  This is done by using quantum mechanics, in the chapter of physics called "Solid State Physics."  The total energy in a point inside the crystal is the result of contributions of all atoms surrounding that point.  The total energy in a point at the surface of the crystal is only the result of contributions of atoms belonging to the crystal.  There are no such atoms outside the surface of the crystal.  Therefore, the total energy at the surface is less than the total energy inside the crystal.  Since in a conductor the electrons can move, they will move spontaneously toward a region of minimum energy which is the surface. In an insulator the energy at the surface is also smaller than the energy inside the bulk.  However, the electrons in an insulator are not "free" to move toward the minimum energy surface region, and will remain strongly bonded to their parent atoms.

## References

### Equations

 Gauss' Law 0 = qenc Electric flux through a Gaussian surface = E dA

### Applications of Gauss's Law

• An excess charge on an isolated conductor is located entirely on the outer surface of the conductor
• The external electric field near the surface of a charged conductor is perpendicular to the surface and has magnitude .  Inside the conductor E = 0.
• The electric field at a point due to an infinite line of charge with uniform linear charge density is in a direction perpendicular to the line of charge and has magnitude: , where r is the perpendicular distance from the line of charge to the point

• The electric field due to an infinite nonconducting sheet with uniform charge density is perpendicular to the plane of the sheet and has a magnitude: • The electric field outside a spherical shell of charge with radius R and total charge q is directed radially and has magnitude: (spherical shell for r R).
Here r is the distance from the center of the shell to the point at which E is measured.  (The charge behaves, for external points, as if it were all at the center of the sphere.)  The field inside a uniform spherical shell of a charge is exactly zero:
E = 0  (spherical shell for r < R)

• The electric charge inside a uniform sphere of charge is directed radially and has magnitude # List of Topics

 Measurements Electric Potential Magnetism Electrical Circuits (AC) Optical Instruments: Mirrors and Lenses Electrostatics Capacitance Sources of Magnetic Fields Maxwell's Equations Interference Electric Fields Current and Resistance Magnetism in Matter Electromagnetic Waves Diffraction Electric Flux Electrical Circuits (DC) Electromagnetic Induction Interaction of Radiation with Matter: Reflection, Refraction, Polarization  ครั้งที่

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