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GATE 2025 EC – Question 49

Electromagnetics · Maxwell's Equations · 2 marks · Multiple choice

A square metal sheet of 4 m × 4 m is placed on the $x$-$y$ plane as shown in the figure below.

If the surface charge density (in μC/m$^2$) on the sheet is $\rho_s(x,y)=4|y|$, then the total charge (in μC, rounded off to the nearest integer) on the sheet is ________.

Diagram for GATE 2025 EC question 49
  1. 16
  2. 85
  3. 64
  4. 256

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Show answer and explanation

Correct answer: (C) 64

Explanation

The sheet spans $-2\le x\le2$, $-2\le y\le2$. $Q=\int_{-2}^{2}\int_{-2}^{2}4|y|\,dy\,dx=4\times\int_{-2}^{2}4|y|\,dy=4\times4\times4=64$ μC, using $\int_{-2}^{2}|y|dy=4$.