Electric Flux and its Dimension

Electric flux is the number of electric field lines or electric force lines that travel across a particular surface area. Electric field lines are thought to start with positive electric charges and end on the negative ones. Negative field lines passing through an area are those that are directed into a closed surface, whereas positive field lines are those that are directed out of a closed surface. Every field line directed into a closed surface continues through the interior and is directed outward somewhere on the surface if there is no net charge within the surface.

The negative flux just equals the positive flux in magnitude, resulting in a net, or total, electric flux of zero. When a net charge is imprisoned inside a solid object, the total flux through the surface is proportional to the enclosed charge, positive if the charge is positive and negative if the charge is negative.

Electric Flux

Gauss’s law for the electric field, one of the fundamental laws of electromagnetic, is a mathematical relationship between electric flux and contained charge. The net flux of an electric field through any closed surface in the metre-kilogram-square system and the International System of Units (SI) is equal to the enclosed charge, in coulombs, divided by a constant known as the permittivity of free space; in the centimetre-gram-square system, the net flux of an electric field through any closed path is equal to the constant 4 times the enclosed charge, in electrostatic units (esu).

It’s worth noting that while charges outside the closed surface have no effect on the electric flux, charges outside the closed surface can have an impact on the net electric field, E, in the Gauss’ Law equation. While Gauss’ Law is true in all scenarios, it is only effective for “by hand” calculations when the electric field has a high degree of symmetry. Spherical and cylindrical symmetry are two examples.

Electric Flux Equation

There is an area connected with all flat surfaces. A well-defined area can be found on a regular geometric surface such as a circle, rectangle, square, or triangle. A surface is mathematically represented by an area vector with a magnitude equal to the measured area and a direction perpendicular to the surface. Therefore,

A =Sn

Where S is the area vector.

The area’s magnitude is A, and 

the unit vector perpendicular to the surface is n.

The electric flux is calculated using the dot product of the electric field vector and the area vector.

  Ø = E.S

Where,

Ø= Electric flux

E stands for electric field.

S: Vector of the area

Equation

Ø = ES cos Ɵ

Symbol: phi or Ø

Volt-metre (V-m) or Newton per metre-squared per Coulomb are SI units (Nm2C-1)

(1 C = 3 x 109 statC) CSG Unit: stat Coulomb (statC) or Franklin (Fr)

[M L3 T3 I-1] Dimensions

When Ɵ = 0 and cos 0 = 1, the result is Ø  = ES.

When placed perpendicular to the electric field, the maximum number of electric field lines will flow through the surface. In addition, if the electric field vector and the area vector are in opposing directions, the electric flux can be negative.

The flux is positive if E and A are in the same direction; otherwise, the flux is negative.

The number of electric field lines travelling through a unit area projected perpendicular to the flow direction is known as the electric flux density. Consider the following equation:

Ø  = ES =

A = 1 and,

Ø =E

As a result, the electric flux density equals the electric field magnitude.

Integral Form

When the electric field is homogeneous and the surface is flat, the equation above applies. The electric field is non-uniform if its magnitude and/or direction change throughout the entire surface. The electric flux is calculated by integrating the dot product over a curved surface with a non-uniform electric field. An infinitesimal area is used for this purpose. The equation gives us the electric flux: 

 ϕ=∫E.dS

Where dA = dA n is the infinitesimal area vector whose direction is perpendicular to the plane and dA = dS n is the infinitesimal area vector whose direction is perpendicular to the surface.

Furthermore, the surface can be curved even if the field is uniform. A curve surface, such as a sphere, cube, or cylinder, can be open or closed. A similar integration is carried out in this scenario as well.

Conclusion

Electric flux is the number of electric field lines or electric force lines that travel across a particular surface area. The environment might be either air or vacuum. A solid conductor might also have it inside or on the surface. The electric field strength in a given location is determined by the number of lines flowing per unit area.

Gauss’s law, often known as Gauss’s flux theorem, is a law that describes the relationship between the distribution of electric charge and the consequent electric field. Gauss’s law, in reality, does hold for moving charges, therefore Gauss’s law is more general in this regard than Coulomb’s law.