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Electric flux
 Gauss's Law
 Gauss's Law for Point Charge
 Gauss's Law for Plane
 Gauss's Law for Magnetism
 Source and Reference

Electric flux

image The source of electric field is charge. When there is electric field flowing radially, there is a source inside. Electric flux is defined as the effect of electric field over the area of the surface projected in a plane perpendicular to the field, that is (𝐸𝑛)𝑑𝐴. In order words, the electric flux of a surface which is parallel to the electric field, is equal to zero. image The electric flux over a surface is (𝐸𝑛)𝑑𝐴.

Gauss's Law

The total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. 𝐸𝑛𝑑𝐴=1𝜀0𝑞inside

Gauss's Law for Point Charge

image For a point charge, the electric flus of concentric spherical surface shell of radius 𝑟 is 𝐸𝑛𝑑𝐴=14𝜋𝜀0𝑞𝑟2(4𝜋𝑟2)=𝑞𝜀0. The electric flux does not depend on the radius of the concentric spherical surface shell because field 𝐸∝1𝑟2 and surface area 𝐴∝𝑟2. image In any segment, the contribution from any shell is the same. image Since electric flux through any outer shell surface is always the same. The electric flux of any closed surface formed by any outer shell surfaces is always the same. image Similarly, by limit the segment to infinite small segment, the enclosed surface can be refined to surround the charge with any smooth shape by following different shperes in different places with the same electric flux.

Gauss's Law for Plane

image For an infinite plane with surface charge density, 𝜎=[𝑄/𝐴]. Due to geometry of plane, the electric filed is perpendicular to plane and has same magnitude everywhere. image Define a Gaussian box, 𝐸 is constant and perpendicular to the two plane surfaces of the Gaussian box. 𝐸𝑛𝑑𝐴=1𝜀0𝑞inside=[𝑄/𝐴]𝐴 𝐸(2𝐴)=1𝜀0𝜎𝐴 𝐸=𝜎𝐴2𝜀0

Gauss's Law for Magnetism

So far, no experiment has found a magnetic charge, i.e. a magnetic monopole. Therefore 𝑞magnet=0 and Gauss's law for magnetism is 𝐵𝑛𝑑𝐴=0

Source and Reference


ID: 200102202 Last Updated: 1/22/2020 Revision: 0

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