GATE 2025 IN – Question 19
An infinite uniform charge sheet with $\rho_s=10\ \mathrm{C/m^2}$ lies in the $z=0$ plane. The surrounding medium has relative permittivity 10. The electric flux density at $P(0,0,5)$, in C/m$^2$, is ______. Unit vectors $\hat a,\hat b,\hat c$ point along $x,y,z$, respectively.
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Correct answer: (A) $5\hat c$
Explanation
By symmetry, the displacement field is normal to the sheet with equal magnitudes on both sides.
Gauss’s law for a pillbox gives $2DA=\rho_sA$.
Therefore $D=\rho_s/2=5\ \mathrm{C/m^2}$.
At positive $z$, the direction is away from the positive sheet: **$5\hat c$ (A)**.
Permittivity changes the electric field $E$, but not this flux-density result.