. E LECTRIC F LUX Consider flow of a liquid with velocity v , through a small flat surface d S , in a direction normal to the surface. The rate of flow of liquid is given by the volume crossing the area per unit time v d S and represents the flux of liquid flowing across the plane. If the normal to the surface is not parallel to the direction of flow of liquid, i.e ., to v , but makes an angle θ with it, the projected area in a plane perpendicular to v is v d S cos θ .
Therefore the flux going out of the surface d S is v. ˆ n d S . For the case of the electric field, we define an analogous quantity and call it electric flux . We should however note that there is no flow of a physically observable quantity unlike the case of liquid flow.
In the picture of electric field lines described above, we saw that the number of field lines crossing a unit area, placed normal to the field at a point is a measure of the strength of electric field at that point. This means that if FIGURE . Field lines due to some simple charge configurations. we place a small planar element of area Δ S normal to E at a point, the number of field lines crossing it is proportional * to E Δ S .
Now suppose we tilt the area element by angle θ . Clearly, the number of field lines crossing the area element will be smaller. The projection of the area element normal to E is Δ S cos θ . Thus, the number of field lines crossing Δ S is proportional to E Δ S cos θ .
When θ = °, field lines will be parallel to Δ S and will not cross it at all (Fig. . ). The orientation of area element and not merely its magnitude is important in many contexts.
For example, in a stream, the amount of water flowing through a