We can caleulate electric us fot a uniforem set of tield lines such as thone in

Question

We can caleulate electric us fot a uniforem set of tield lines such as thone in the image by riasing the field lines in a region with an electric field vector that points paralel t the lines. In the image above, the uniform electris i t iseetion of the eld field associated with these field lines conulid be We can also define an "area vector" for "ach skle of dr shape tha the fiel l lius ate Bowing through. In the image below, two of these vectors are drawn in yellow, while the electric field vectors are depicted in red: Notice that the area vectors are always shown as pointing outward, away from the inner volume of the shape. Electric flux for a uniform field through a flat surface is calculated by where A is the area vector of the surfce and E is the electric field at a point at the center of that surface Question 2.4) The dot product takes into account the angle between the two vectors. What is the physical significance of this with reference to the image above? How does taking into account the angle ensure that the electric flux out of the two sides will have the same magnitude (as you determined earlier by simply counting the field lines)?

Explanation / Answer

The angle between the two vector also decide the amount of field line passing through the surface. When angle is zero, then maximum field line will pass while when angle is ninty, no field line will pass.

In the given figure, right face has larger area but the angle is greater than zero (cosine of angle will be less) while left face has smaller area but angle zero (cosine will be max i.e. 1) hence effectively both sidde flux through the surface will be same.

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