Collegedunia Team Content Curator
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Electric flux is the measure of the flow of electric field through a surface. Mathematically, electric flux is defined as the dot product of electric field and area vector of the surface.
Consider a small area element dA on a surface with an electric field E. The electric flux dΦ through this area element is given by:
| dΦ = E · dA |
where · represents the dot product of E and dA. The electric field E is perpendicular to the area element dA, so the dot product of E and dA is simply the product of their magnitudes.
| dΦ = E dA cos θ |
where θ is the angle between the direction of the electric field and the normal to the surface. Since the electric field is perpendicular to the surface, the angle θ is 0 degrees and cos θ is 1. Therefore, we can simplify the equation to:
| dΦ = E dA |
Now, to find the total electric flux Φ through the entire surface, we integrate the electric flux over the entire surface area A:
| Φ = ∫ E · dA |
where the integral is taken over the entire surface. This is the mathematical expression of electric flux.
In summary, the electric flux Φ through a surface is given by the dot product of the electric field E and the area vector dA.
Electric Flux Derivation Example
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