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NCERT Class XII Chapter
Electric Charges and Fields
Questions With Solutions

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Question : 18 of 34
Marks: +1, -0
A point charge +10 μC is at a distance of 5 cm directly above the centre of a square of side 10 cm, as shown in figure. What is the magnitude of the electric flux though the square?
Solution:  
Let us assume that the given square be one face of the cube of edge 10 cm.
As charge of +10 μC is at a distance of 5 cm above the centre of a square, so it is enclosed by the cube.
Hence by Gauss’s theorem, electric flux linked with the cube is
ϕ = qε0\frac{q}{\varepsilon_0} = 10×1068.85×1012\frac{10 \times 10^{-6}}{8.85 \times 10^{-12}} = 1.13 × 10610^6 N m2C1\mathrm{m}^2\,\mathrm{C}^{-1}
So, the magnitude of the electric flux through the square is
ϕsq\phi_{\mathrm{sq}} = ϕ6\frac{\phi}{6} = 1.136\frac{1.13}{6} × 10610^6 or ϕsp\phi_{\mathrm{sp}} = 1.9 × 10510^5 N m2C1\mathrm{m}^2\mathrm{C}^{-1}
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