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The total flux related to a closed surface is equal to 1/ε0 times the charge encompassed by the closed surface, according to the Gauss law. The charge limited when divided by the permittivity equals the total electric flux out of a closed surface. The formula for calculating electric flux through an area is by multiplying the electric field by the surface area reflected in a plane perpendicular to the field. Gauss’s Law is a common principle that can be applied to any closed surface. It is a useful tool since it allows you to estimate how much confined charge there is by projecting the field on a surface outside of the charge distribution. It aims to simplify the estimation of the electric field by using geometries with appropriate symmetry.
Electric Flux
In association with Gauss’s Law, the theory of electric flux is useful. The electric flux throughout a planar area is calculated by multiplying the electric field by the area component perpendicular to the field. If an area is not planar, the flux must be evaluated using an area integral because the angle will be changing all the time.
An electric field’s electric flux is a significant element. It can be thought of as the number of forces colliding in a particular area. Electric field lines are generally thought to commence with positive charges and stop with negative charges. Negative field lines are regulated into a closed surface, whereas positive field lines are conducted out of a closed surface.
Applications of Electric Flux in Daily Life
Electric flux is the foundation of electrostatics in physics and has a wide range of applications, including:
The electric field can be determined with the help of electric flux.
Electric flux makes it easier to assess the electric field in complex figures.
The Gauss theorem is one of the most useful electrostatic theorems, and is specified mostly on electrostatics.
The determination of the electric field is aided by electric flux. Electric flux makes it easier to assess the electric field in complicated figures.
Electric flux observation:
Whenever the electric field is parallel to the surface area S, the angle comes to be 90°, and when the value of cos 90° is zero, electric flux is zero.
The area vector has both magnitude and direction and determines the direction of S.
When the electric field and surface vector are antiparallel, the electric flux becomes negative.
The area vector’s direction is always away from the surface.
Electric Flux Calculator
Electric flux calculator or the formula for calculating electric flux:
The Gauss Law for the electric field is the mathematical relationship involving electric flux and the enclosed charge. The net flux of an electric field through every surface that is closed is usually equivalent to the enclosed charge, in coulombs, divided by a constant termed the permittivity of free space in the associated meter-kilogram-second system and the international System of Units or SI.
The net flow of an electric field through any closed surface in the centimeter-gram-second system is equal to 4π times the contained charge with electrostatic units. The quantity of electric field lines passing through a virtual surface determines the electric flux. A formula can help you grasp this:
The electric flux (ΦE) travelling through a surface of vector area S is as follows if the electric field is uniform:
ΦE = E·S = EScosθ
where,
E is the electric field’s magnitude in units of V/m
S is the surface’s area
θ is the angle between the electric field line and the normal or perpendicular to S.
The electric flow dE through a small surface area dS in a non-uniform electric field is commonly indicated by:
d ΦE = E·dS
Where,
E = electric field multiplied by the component of the area perpendicular to the field.
Electric Flux Calculator Examples:
1) A planar surface has an area of 1 m2, if an electric field crosses with an angle of 30° to it, and has E= 2 V/m. Find the electric flux?
Answer:
From the formula of the electric flux,
Φ = E A cos(θ) = 2 V/m * 1 m2 * cos(30°)
Φ = 1 V m
2) Find the electric flux when a planar surface has an area of 0.25 cm2, if an electric field crosses perpendicular to it, and has E= 2 V/m.
Answer:
From the formula of the electric flux,
Φ = E A cos(θ) = 2 V/m * 2.5 * 10(-5) m2 * cos(0°)
Φ = 5*10(-5) V m
While charges outside the closed surface do not affect the electric flux, charges outside the closed surface can alter the net electric field, E, in Gauss’s law calculation. While Gauss’s law is adequate in all procedures, it is most effective for “by hand” analyses when the electric field has a great degree of symmetry. Cylindrical and spherical symmetry are two examples.
Conclusion
Electric flux is defined as multiple electric field lines traveling across a given area in electrostatics. It’s a new physical quantity that is used to calculate the strength of an electric field and create the foundations of electrostatics in physics. Because it is dependent on the direction of the electric field and the orientation of the planar object, electric flux is a changeable quantity. Electric flux becomes zero when the electric field is parallel to the surface area ∆S, when the angle becomes 90°, and the value of cos 90° is zero, according to observations. When the electric field and area vector are antiparallel, the electric flux becomes negative. The area vector’s direction is always out of the surface.
