A point charge \( q \) is held at a distance \( d\) above an infinite grounded conducting plane . A certain amount of charge is induced on the grounded conductor due to the presence of the point charge . Considering the grounded conductor to be in the \(x-y \) plane and the point charge q at \( ( 0,0, d) \) , evaluate the surface charge density \( \sigma (x,y) \) induced on the conducting plane . Enter the answer as the value (with sign) of \( ( \sigma ( 3,4 ) × 10^3 ) \) in \( C/m^2 \)

**Details and assumptions** :

• \( d = 5 m \)

• \( q = 1 C \)

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