Area Vector, Solid Angle and Electric Flux
Dependence of flux on the inclination between E and nThe inclination between and is a measure of the number of field lines crossing the area element in which the electric field acts. Thus, the number of field lines crossing is proportional to .
Electric fluxElectric flux is the measure of flow of the electric field through a given area. Electric flux is proportional to the number of electric field lines going through a normally perpendicular surface.
Solid angleA solid angle (symbol: ) is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large the object appears to an observer looking from that point.
An object's solid angle in steradians is equal to the area of the segment of a unit sphere, centered at the angle's vertex, that the object covers.
Relation between electric field lines and flux across a surfaceThe field lines carry information about the direction of electric field at different points in space. Having drawn a certain set of field lines, the relative density (i.e., closeness) of the field lines at different points indicates the relative strength of the electric field at those points. The field lines are crowded where the field is strong and are spaced apart where it is weak.
While electric flux is the measure of the flow of the electric field through a given area. It is proportional to the number of electric field lines passing normally through a perpendicular surface.
Define and calculate electric flux density and identify its unitThe Electric Flux Density (D) is related to the Electric Field (E) by:
In Equation , is the permittivity of the medium (material) where we are measuring the fields.
The Electric Field is equal to the force per unit charge:
Then the Electric Flux Density is:
From Equation , the Electric Flux Density is very similar to the Electric Field, but does not depend on the material in which we are measuring (that is, it does not depend on the permittivity. Note that the field is a vector field, which means that at every point in space it has a magnitude and direction.
The Electric Flux Density has units of Coulombs per meter squared .
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