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Field at a point due to an infinite charged sheet and a parallel line charge

This type of question, asked 2 times: 13 Apr 2023, 4 Apr 2024. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    13 Apr 2023

    26
    A thin infinite sheet charge and an infinite line charge of respective charge densities +σ+ \sigma and +λ+ \lambda are placed parallel at 5 m5\text{ }m distance from each other. Points ' PP ' and ' QQ ' are at 3πm\frac{3}{\pi}m and 4πm\frac{4}{\pi}m perpendicular distance from line charge towards sheet charge, respectively. ' EPE_{P} ' and ' EQE_{Q} ' are the magnitudes of resultant electric field intensities at point ' PP ' and ' QQ ', respectively. If EPEQ=4a\frac{E_{P}}{E_{Q}}=\frac{4}{a} for 2∣σ∣=∣λ∣2|\sigma| = |\lambda|. Then the value of aa is____

  2. Question 2

    4 Apr 2024

    21
    An infinite plane sheet of charge having uniform surface charge density +σsC/m2+\sigma_{s}C/m^{2} is placed on x−yx - y plane. Another infinitely long line charge having uniform linear charge density +λeC/m+\lambda_{e}C/m is placed at z=4 mz = 4\text{ }m plane and parallel to yy-axis. If the magnitude values ∣σs∣=2∣λe∣\left| \sigma_{s} \right|= 2\left| \lambda_{e} \right| then at point (0,0,2)(0,0,2), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is πn:1\pi\sqrt{n}:1. The value of nn is ______.