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Electric Flux of a Non-Uniform Field

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A non-uniform electric field is given by the expression E⃗=(2xy)i^+(x2)j^+(3z)k^\vec{E} = (2xy)\hat{i} + (x^2)\hat{j} + (3z)\hat{k} N/C. What is the electric flux through a 2 m×4 m2~\mathrm{m} \times 4~\mathrm{m} rectangle that lies in the xz-plane and is centered at the origin?

A

83\frac{8}{3} N·m²/C

B

4 N·m²/C

C

12 N·m²/C

D

0 N·m²/C

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