Electric Field Intensity Due To a Infinite Sheet Charge - Field Theory.


(SYMMETRY ABOUT A PLANE)

- Consider an infinite sheet of charge in the y-z plane having a uniform charge density of ρs C/m2.


- For easy analysis, divide the sheet into differential width strips (dy).


ρL = ρs dy

- The distance between the point P and the line charge
Z2 = X2 + Y2

- Since the sheet lies in y-z plane the field components due to y and z will be canceled out at the point at which the field is to be determined.
(As we have seen in electric field due to a line charge where the z component gets canceled out.)


- Only Ex component is present and hence the field is a function of x alone for an infinite sheet of charge on y-z plane.


- Hence the electric field intensity due to an infinite line charge is given as:



- Magnitude Ex at point P due to an infinite differential width strip(dy):


from – to + ,



- If the field intensity is obtained at point P on the negative axis, then E will be:



- In general, Electric field intensity for an infinite sheet of charge is given as:




Where an is a unit vector normal to the sheet.


- The electric field intensity (E) points away from the plane if ρs is positive and towards the plane if ρs is negative.


- The magnitude of the electric field is a constant – the magnitude is independent of the distance from the infinite plane.


- This is because no matter how far the point is from the infinite sheet, the distance becomes incomparable with the dimensions of the plane. Hence it seems the point is very close to the infinite plane.


- In a parallel plate capacitor the electric field intensity between the two plates having equal and opposite charge is given by:


The first –ve sign denotes –ve charge on one plate and the second –ve sign denotes opposite direction.



ALSO READ:

- Introduction To Electrostatics.

- Coulomb's law.

- Electric Field Intensity (E).

- Electric Lines Of Forces /Streamlines / Electric Flux (ψ) .

- Electric Flux Density (D).

- Electric Field Intensity Due To a Finite and Infinite Line Charge.

- Electric Field Intensity Due To a Infinite Sheet Charge.

- Electric Field Intensity Due To a Circular Ring Charge.

- Electric Field Intensity Due To a Circular Disk Charge.

- Numericals / Solved Examples - Electric Force and Field Intensity.

- Numericals / Solved Examples - Electric Field Intensity - Line, Surface and Mixed Charge Configuration.


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8 comments:

  1. thanks.learned a lot. but can you give any examples for solving an electric field at point given a finite sheet?

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  2. Excellent presentation, 3D picture in 2D.
    Easy to understand , Once read will never forget.

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  3. in an electric field due to infinite sheet of charge, the distance of the charge is not considered. is there a physical interpretation to this?

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  4. excellent explanation!!

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  5. me too...... searching about the physical interpretation of e.f if the electric field due to infinite sheet is independent of distance . if it is so the the field produced must experienced all over the world equally..? plz help me ..... if u can

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