A thin infinite sheet charge and an infinite line charge of respective charge densities $+ σ$ and $+ λ$ are placed parallel at 8 m distance from each other. Points 'P' and 'Q' are at $\frac{3}{π} m$ and $\frac{4}{π} m$ perpendicular distances from line charge towards sheet charge, respectively. ' $E_{P}$ ' and ' $E_{Q}$ ' are the magnitudes of resultant electric field intensities at point 'P' and 'Q' respectively. If $2 |σ| = |λ|$ , the ratio of $\frac{E_{P}}{E_{Q}}$ is ___________

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8:9

3:2

9:8

2:3

answer is A.

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Detailed Solution

$E_{P} = \frac{2 K λ}{r} - \frac{σ}{2 ε_{0}} E_{P} = \frac{σ}{2 ε_{0}} - \frac{2 σ}{6 ε_{0}} = \frac{σ}{6 ε_{0}}$

Similarly, $E_{Q} = \frac{σ}{2 ε_{0}} - \frac{2 σ}{2 π ε_{0} (\frac{4}{π})} = \frac{σ}{4 ε_{0}}$

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