Electric Field Intensity Due To a Circular Disk Charge - Field Theory.


Electric Field Intensity Due To a Circular Disk Charge - Field Theory.

- Consider a circular disc of radius ‘a’ which carries a uniform surface charge density ρs , C /m2.


- Say the disk lies on x-y plane (or z = 0 plane) with its axis along the z axis as shown in the figure.


- We need to find out electric field (E) due to a circular disk at a point P (0, 0, h) on the z axis (z > 0).


- Electric field intensity (E) at a point due to any surface charge (ρs) is given as:









- Consider the triangle shown in figure(Since it’s a disc, the varying terms are radius ρ and angle φ)

As per the vector law of addition,

ρ aρ + R = h az → R = - ρ aρ + h az

| R | = (ρ2 + h2)1/2

aR = R / | R |


aR = - ρ aρ + h az / (ρ2 + h2)1/2


Substituting all these values in the above equations, the electric field intensity E becomes

Electric Field Intensity Due To a Circular Disk Charge - Field Theory.

- Contribution along aρ due to symmetry adds up to zero.

- Therefore the final electric field intensity at point (0, 0, h) has only z component.

Electric Field Intensity Due To a Circular Disk Charge - Field Theory.


- As a → 0, the electric field intensity (E) also tends to zero i.e. E → 0


Electric Field Intensity Due To a Circular Disk Charge - Field Theory.


- Hence electric field intensity (E) at point (0, 0, h) is given as:


Electric Field Intensity Due To a Circular Disk Charge - Field Theory.



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.

- Short Notes/FAQ's

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Comments

  1. AnonymousMarch 27, 2011 at 11:13 PM

    It is not in agreement with ISAT prescribed Formula for the same in the solutions

    ReplyDelete

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