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GATE ECE 2025 | Question: 39

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A square metal sheet of $4 \mathrm{~m} \times 4 \mathrm{~m}$ is placed on the $x-y$ plane as shown in the figure below.

If the surface charge density (in $\mu \mathrm{C} / \mathrm{m}^{2}$ ) on the sheet is $\rho_{s}(x, y)=4\mid y \mid$, then the total charge (in $\mu \mathrm{C}$, rounded off to the nearest integer) on the sheet is $\_\_\_\_\_\_$

  1. $16$
  2. $85$
  3. $64$
  4. $256$

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