Can the Prince save you now?

Gauss' law is a very powerful method to determine the electric field due to a distribution of charges. It can, for instance, be used to find the electric field due to an infinite plate. However, it is usually useless whenever there is a non-uniform field, i.e. there is broken symmetry.

One such case is that of a finite rectangular plate. Find the electric field due to a uniformly charged rectangular plate at a point 1 m above its center of mass.

Details And Assumptions

  • Length = 138m\sqrt{\dfrac{13}{8}}\text{m}
  • Breadth = 3 m
  • Total Charge on plate = 8×108C 8 \times 10^{-8} \text{C}
  • k=9×109Nm2C2k=9 \times 10^9 \frac{\text{Nm}^2}{\text{C}^2}
  • Plate is an Insulator
This is an original problem.

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