Application Of Gauss Law To A Uniformly Charged Sphere - Field Theory.


- Consider a sphere of radius “a” having a uniform volume charge density of ρo C/m3.


- Gaussian surface selected for a symmetric sphere charge is a sphere itself.


- Here we consider two cases:
  • A Gaussian surface with a radius r < a.
  • A Gaussian surface with a radius r > a.





CASE 1:

If r < a (consider the 1st figure), the total charge enclosed by the Gaussian surface is:











Electric flux is given as:













Here ds is taken to be a function of θ and φ( since the surface is a hollow sphere).


Gauss law states that Ψ = Qenc

Therefore,

Dr 4π r2 = (4 / 3) (ρo πr3)

              Or

D = (r / 3) ρo ar (0 < r < a) 



CASE II: 

If r > a (consider the above figure), the total charge enclosed by the Gaussian surface is:












Electric flux is given as:












 Gauss law states that Ψ = Qenc


Therefore,

Dr 4π r2 = (4 / 3) (ρo πa3)

              Or

D = (a3 / 3r2 ) ρo ar (r > a)


ALSO READ: 

- Gauss's Law - Theory.

- Gauss's Law - Application To a Point charge.

- Gauss's Law - Application To An Infinite Line Charge.

- Gauss's Law - Application To An Infinite Sheet Charge.

- Gauss's Law - Application To a Uniformly Charged Sphere.

- Numericals / Solved Examples - Gauss's Law.

- Scalar Electric Potential / Electrostatic Potential (V).

- Relationship Between Electric Field Intensity (E) and Electrostatic Potential (V).

- Electric Potential Due To a Circular Disk.

- Electric Dipole.

- Numericals / Solved Examples - Electric Potential and Electric Dipole.

- Energy Density In Electrostatic Field / Work Done To Assemble Charges.

- Numericals / Solved Examples - Electrostatic Energy and Energy Density.

- Numericals / Solved Examples - Gauss's law...



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