Therefore electric flux will be a 1 Volt Meter. If an electric field crosses with an angle of \(60^\) to it and has E= 2 Volte per meter. If the net flux through a gaussian surface is zero, the following four statements could be true. 24 CHAPTER OUTLINE 24.1 Electric Flux 24.2 Gausss Law 24.3 Application of Gausss Law to Various Charge Distributions 24.4 Conductors in Electrostatic Equilibrium 24.5 Formal Derivation of Gausss Law Gausss Law ANSWERS TO QUESTIONS. Q.1: A planar surface has an area of 1 square meter. The angle between the plane and the axis parallel to the direction of flow of the electric field. Similar to the above example, if the plane is normal to the flow of the electric field, the total flux is given as:Īlso, if the same plane is inclined at an angle \theta, the projected area can be given as \(Acos\theta\) and the total flux through this surface will be, The total number of electric field lines passing through a given area in a unit time is the electric flux. Example based on Gausss Law has been experimentally observed that the electric field in a large region of earths atmosphere is directed vertically down. positive if it is positive, negative if it is negative. But flux is also equal to the electric field E multiplied by the area of the surface. If a net charge is contained within a closed surface, then the total flux through the surface will be proportional to the enclosed charge, i.e. Gauss' law tells us that the flux is equal to the charge Q, over the permittivity of free space, epsilon-zero. So, the net or total, the electric flux will be zero. The negative flux is just equal to the magnitude of the positive flux. If there is no given net charge within some closed surface then every field line directed into the given surface will continue through the interior. Therefore it is analogous to the flow of liquid as discussed above. The electric field is behaving in a similar way. Here, \(dA cos\theta\) is the projected area of the plane towards the perpendicular direction of the flow of the liquid. This helps us define the flux to be the dot product of electric field and the area. For open surfaces, we have to arbitrarily choose between two perpendiculars, but for closed surfaces, we choose the outward direction as our standard. Then the total volume of liquid crossing through the plane per unit time is given as \(v ×dA \ cos \theta\). The direction of area vector is always perpendicular to it. When the plane is not exactly normal to the flow of the fluid then it will be inclined at an angle \(\theta\). Then the volumetric flow of the liquid crossing that plane normal to the flow will be given as v × dA. Let us consider a small unit area of the plane given as dA. We will take the cross-sectional plane of the pipe. In (c), the charges are in spherical shells of different charge densities, which means that charge density is only a function of the radial distance from the center therefore, the system has spherical symmetry.2 Solved Examples Electric Flux formula What is electric Flux?Ĭonsider the flow of water with some velocity v in a pipe in a certain fixed direction, suppose towards the right. In (b), the upper half of the sphere has a different charge density from the lower half therefore, (b) does not have spherical symmetry. In (a), charges are distributed uniformly in a sphere. The spherical symmetry occurs only when the charge density does not depend on the direction. Charges on spherically shaped objects do not necessarily mean the charges are distributed with spherical symmetry. Different shadings indicate different charge densities. In addition, since the electric field is a vector quantity, the electric field is referred to as a vector field. \): Illustrations of spherically symmetrical and nonsymmetrical systems. In the case of the electric field, Equation 5.5.6 shows that the value of E (both the magnitude and the direction) depends on where in space the point P is located, measured from the locations ri of the source charges qi.
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