Electric flux1/21/2024 ![]() ![]() In this case, the flux is given by:įurthermore, as you can see in the figure, the vector d S is parallel to u r at any point of the sphere. ![]() We are going to calculate the flux in the situation (a) represented in the figure, with the sphere’s center is co-located with the charge. As you can see in the figure, the number of field lines passing through the sphere (flux) is independent of its position. We have represented in red a sphere of radius r that we will use as the Gaussian surface through which we will calculate the flux of the electric field. ![]() Let’s consider a positive point charge and the electric field lines due to it as the ones that are represented in the next figure. Question: Consider a uniform electric field E 3 × 103 i N/C. Notice that the unit of electric flux is a volt-time a meter. We are going to demonstrate Gauss’s law for a point charge. Solution: The electric flux which is passing through the surface is given by the equation as: E E.A EA cos. The closed surface through which the flux is calculated is called a Gaussian surface. Electric flux definition: the product of the electric displacement and the area across which it is displaced in an. The net electric flux through any hypothetical closed surface is equal to the net electric charge within that closed surface divided by the vacuum permittivity ε 0. As the angle between the two decreases, its cosine increases until the situation represented in (d) where the cosine is 1 and therefore the flux passing through the plane is maximum. With the definition of the dot product we get:Īs you can see in the first figure (a), when the angle between E and d S is 90 0, its cosine is zero and therefore the flux passing through the surface is zero. It is another physical quantity to measure the strength of electric field. This explains why the flux definition includes an integral (or, and it is the same, a sum). Electric Flux is defined as a number of electric field lines, passing per unit area. To calculate the flux passing through any surface, we decompose it into surface elements, we calculate the flux for each one of them and then we sum all these contributions. But in the general case, vector d S will be different at each point of the surface. In the last two examples, the perpendicular vector to the (plane) surface always had the same orientation. ![]() If we represent the surface using a vector d S perpendicular to it at any point and with its magnitude equal to the surface area, the flux of the electric field is defined as: The mathematical operator used to “count” the number of field lines passing through a certain surface is the dot product. The net flux through the surface represented in the next figure is zero: In the figure, no lines pass though the surface in (a), but the number of lines passing through it increases as the surface is inclined, with a maximum in (d).įurthermore, to count the net number of field lines passing through a surface, we need to consider their direction. As you can see, the number of field lines passing through a surface (it is a plane in this example), is dependent upon the orientation of the field lines with respect to the surface. The next figure represents in green any electric field. The question is therefore, how can we count the field lines passing through a surface? Gauss’s law is based on the concept of flux of field lines Φ, defined as the number of lines passing through a certain surface. It is used to calculate the electric field due to a continuous distribution of charge in particular when there is some symmetry in the problem. In that case, the direction of the normal vector at any point on the surface points from the inside to the outside.Gauss’s law is an other way to express Coulomb’s law that quantifies the amount of force between two stationary electrically charged particles or the electric field due to a point charge. However, if a surface is closed, then the surface encloses a volume. (c) Only \(S_3\) has been given a consistent set of normal vectors that allows us to define the flux through the surface. (b) The outward normal is used to calculate the flux through a closed surface. \): (a) Two potential normal vectors arise at every point on a surface. ![]()
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