electric flux equation for gaussian surface

#Electric flux equation for gaussian surface free#

It was initially formulated by Carl Friedrich Gauss in the year 1835 and relates the electric fields at the points on a closed surface and the net charge enclosed by that surface. It is one of the four equations of Maxwell’s laws of electromagnetism. We can also use Gauss’s Law to find the electric flux passing through a closed surface.Gauss’s law states that the net flux of an electric field in a closed surface is directly proportional to the enclosed electric charge.All these charge distributions are symmetrical in nature. Gauss’s Law can be used to find the electric field of point charge, infinite line of charge, infinite sheet of charge or sphere of charge.The magnitude of the field must be constant.The shape of the surface may be irregular but it must be large to enclose the charge.Any Gaussian surface has to satisfy the following conditions. This means that the electric flux passing through a closed surface is independent to shape or area of the surface.Ī Gaussian Surface is a special surface over which the Gauss’s Law can be applied.

#Electric flux equation for gaussian surface free#

Gauss’s Law states that the electric flux passing through a closed surface is equal to the ratio of total charge enclosed by that surface to the permittivity of free space. But what if there are some charges inside the volume of the surface? The answer to this lies in Gauss’s Law. Then the surface is divided into small elements of area d and the integral of the flux is taken for the entire surface.Īfter understanding the concept of Electric Flux, we can say that in a closed surface, if there are no charges inside its volume, then electric flux through the surface is zero. This formula is well and good if the surface has a deterministic area. Therefore, the units of Electric Flux are Newton meter 2 / Coulomb (Nm 2/C). Where, E is Electric Field with units Newton. the electric field and the area of the surface, the equation of flux can be written as follows: In general, if θ is the angle between the electric field vector and surface vector of the surface with area A, then number of field lines passing through this surface is proportional to cos (θ).Ĭonsidering the other two factors i.e. If the surface is parallel to the field, then the number of field lines passing through the surface is zero.īut if the surface is placed at an orientation angle of θ, then the number of line passing will be proportional to this angle. When the surface is perpendicular to the electric field, maximum number of lines are intercepted by the surface. To understand this more, let us consider a surface, which is inserted through electric field in three different orientations.

The first two points are pretty obvious but the interesting point here is the orientation of the surface. Orientation of the surface with respect to the lines of force.Then exploring further, the lines of force passing through a surface of a given area is dependent on three factors: The concept of flux is always associated with something (electric field, in this case) going through a given area.

Electric Flux is defined as the total number of lines of electric force in any particular electric field. Electric Flux is the total number of tubes of flux in an electric field i.e. This bunch or small closed area is called a Tube of Flux. According to his studies, electric field is composed of small bunches of electric lines of force, which are fixed in number. The field lines or flux lines can be used to pictorially represent the distribution of Electric Flux around a charge.īased on the experiments performed by Michael Faraday in late 1830’s, Electric Field around a charge can be imagined as presence of lines of force around it. The Electric Field, imagined to be present around a charge, can be represented in terms of a quantity known as Electric Flux.

Normally, the flux lines enter or leave a charged surface.

All the flux lines are parallel to each other.

The strength of the electric field is dependent on the number of flux lines.

Flux lines generally originate at positive charges and terminate at negative charges.

These lines of force are called Field Lines or Flux Lines.Įlectric Field or Flux Lines are the lines of force around a charge with the following properties: The direction of this force can be represented by lines that are radially coming out of a positive charge or going in towards a negative charge. In the above example, a unit test charge ‘q’ placed near a point charge ‘Q’ experiences the force. Electric Field is defined as the force per unit charge at a particular point.įor example, the Electric Field of a point charge ‘Q’ on a test charge ‘q’ at a distance is given by Before going further into the main topics of discussion, let us quickly recap some of the important concepts.