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GATE EC 2022 Set 1 — Question 65

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NAT+2 / -0MediumDifferential & Integral FormsMaxwell's EquationsElectromagneticsGauss, Stokes & Green's TheoremsVector CalculusEngineering Mathematics

Electromagnetics → Maxwell's Equations → Differential & Integral Forms

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Question

In an electrostatic field, the electric displacement density vector, D⃗\vec{D}, is given byD⃗(x,y,z)=(x3i⃗+y3j⃗+xy2k⃗) C/m2,\vec{D}(x, y, z) = (x^3 \vec{i} + y^3 \vec{j} + xy^2 \vec{k}) \text{ C/m}^2,where i⃗,j⃗,k⃗\vec{i}, \vec{j}, \vec{k} are the unit vectors along xx-axis, yy-axis, and zz-axis, respectively. Consider a cubical region RR centered at the origin with each side of length 1 m, and vertices at (±0.5 m,±0.5 m,±0.5 m)(\pm 0.5 \text{ m}, \pm 0.5 \text{ m}, \pm 0.5 \text{ m}). The electric charge enclosed within RR is \text{_________} C (rounded off to two decimal places).
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