In the figure below there are two examples, on the left a curved surface and on the right a closed surface.įigure 3. Previously, the electric field flux was determined in the particular case of a uniform field incident on a flat surface. For a surface of arbitrary shape S and / or a non-uniform electric field, the angle between E and n can vary from point to point. Electric field flux on an arbitrary surface Examples of electric field flux with different orientations between the field and the surface normal vector. These possibilities are shown in the following image: Figure 2. On the other hand, if the angle between E and n is equal to 0, the flow acquires its maximum value. Null when θ is exactly 90º, because cos 90º = 0 and the field lines in this case are tangential to the surface. Negative if said angle is greater than 90º, because then cos θ is less than zero. Positive when the angle θ between E and n is less than 90º, since cos θ is greater than zero. ExamplesĪccording to the definition, the electric flux can be positive, negative or equal to 0. The unit for electric field flux in the SI International System of Units is Nm 2 / C (newton x square meter / coulomb). Alternatively, since the field is also measured in V / m (volt over meter), the electric flux remains in (V ∙ m). This expression is consistent with the scalar product between the vectors E and n : On the other hand, the electric field flux also depends on the magnitude of E , since the larger this is, the more field lines cross the surface. And of course, the greater the area S of said surface, the greater the flow, so the following equation is established: In the figure above a flat surface crossed by an electric field shown E . When the unit vector normal to the surface n and the field E are parallel, the number of field lines through the surface is maximum. But as the angle θ between n and E increases , the number of lines that pass through the green surface is less. Electric field flow through a flat surface.
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