Give Mathematical Derivation of electric flux =E. ds.

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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

Electric Flux Derivation Example

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Give Mathematical Derivation of electric flux =E. ds.

CBSE CLASS XII Related Questions

2.
Two copper wires having their radii in the ratio of 3 : 2 are connected in series across a battery. Find the ratio of the drift velocities of the electrons in the wires.

3.
This ‘average velocity’ is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ?

4.
Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.

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Give Mathematical Derivation of electric flux =E. ds.

CBSE CLASS XII Related Questions

2.Two copper wires having their radii in the ratio of 3 : 2 are connected in series across a battery. Find the ratio of the drift velocities of the electrons in the wires.

3.This ‘average velocity’ is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ?

4.Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

2.
Two copper wires having their radii in the ratio of 3 : 2 are connected in series across a battery. Find the ratio of the drift velocities of the electrons in the wires.

3.
This ‘average velocity’ is found be few mm/s for currents in range of a few amperes. How then is current established almost the instant a circuit is closed ?

4.
Derive an expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d with air present between the plates.